2 pounds skinless, boneless chicken breasts, (or tenders)
6 ounces shiitake mushroom caps
1 cup flour, or more, for dredging
3 tablespoons extra-virgin olive oil, more if needed
For the Sauce
3 tablespoons soft butter
1 cup tomato sauce, marinara sauce, or a few tablespoons tomato paste
1/4 teaspoon peperoncino
1 cup white wine
6 fresh sage leaves, shredded
6 ounces/slices Fontina cheese, enough to top all the chicken cutlets
3/4 cups grated Parmigiano-Reggiano
1 cup vegetable or chicken stock, hot
Preparing the Chicken and Mushrooms
Place a rack in the center or upper third of the oven and preheat to 425 degrees.
If the chicken breasts are whole, cut them in half. Trim off any bits of fat, skin or tendon. Flatten each breast half with a mallet (or the flat bottom of a heavy pan) to an even thickness, about 3/4-inch.
Trim the stems from the mushrooms and brush them clean or wash them if necessary. You will need enough mushroom caps to cover the chicken in a single layer.
Put 3 tablespoons of the olive oil into the skillet, tilt to coat the bottom and set it over medium heat.
In a single layer, place the mushroom caps into the preheated pan. Keep the heat moderate and let the pieces caramelize slowly for a few minutes. Turn when the edges are nicely browned on the underside; fry for about 2 minutes on the second side. With a slotted spatula, lift the pieces to a plate or tray (no paper towels are needed here) and salt lightly. Fry the remaining mushroom caps in the same way and salt them. While frying, monitor the heat, keeping it high enough to brown the mushrooms but not let them burn. When the mushrooms are done, turn off the heat but leave all the oil in the skillet.
Starting on the Stovetop
Have all of your gratinate and sauce ingredients handy to the stove. You should have at least 2 tablespoons of olive oil in the skillet (add a bit if needed). Add 1 tablespoon of the butter and set the pan over low-medium heat.
Salt the chicken pieces lightly, flop them in the dredging flour to coat on both sides, and pat off excess. When the butter is just beginning to sizzle, arrange all six cutlets in the pan. Cook them gently for a minute and a half, and then turn them over; they should be very lightly colored, with no browning.
Maintain the gentle cooking while you assemble the gratinate. Sprinkle the chicken again with salt (using 1/2 teaspoon total for the dish).
Spread a heaping tablespoon of tomato sauce (if using sauce, do not put tomato paste here) on top of each cutlet. Arrange the mushroom caps on top of the sauced chicken, overlapping them so each portion is neatly covered. Use all the mushrooms.
Now raise the heat a bit and begin to develop the sauce: Sprinkle the peperoncino onto an open hot spot where it will sizzle and toast briefly. If using tomato paste, drop a tablespoon or two into the pan, smearing it on the bottom of the pan.
Drop the remaining butter, in small pieces, in between the layered cutlets. After a few seconds, pour in 2/3 cup of the wine around the cutlets and let it heat briefly, 10 to 20 seconds.
Spoon the rest of the cup of tomato sauce into the pan (not on the chicken). Bring to a simmer, and then drop the sage into the sauce all around the pan.
Give the pan a gentle shake, or two, to mix and emulsify the sauce ingredients. Finally, sprinkle two tablespoons of grated cheese evenly over each mound. At this point, the sauce should be about 1/3-inch deep in your pan or even higher, coming well up the sides of the chicken cutlets. If not, pour in the rest of the wine and as much hot water or stock as necessary. Raise the heat again to bring the pan sauce to an active simmer.
Finishing in the Oven
When the sauce is simmering, place the skillet in the oven. (Put the handle in front and the food in the back).
Bake for about 10 minutes-and have thick pot holders or dry towels in hand before you touch the handle or the skillet!-then open the oven and check the pan.
Right on the rack; give the skillet another gentle shake. There should still be plenty of sauce and the cheese should be lightly colored. If the sauce appears syrupy, or close to evaporating, add more herb water, stock, tomato sauce or wine to raise the level. Bake for another 8 to 10 minutes, until the chicken is fully cooked and tender and the grattinata top is deeply and evenly browned. If the cheese layer still appears too light, raise the heat in the oven as high as possible (turn on the broiler if it is top-mounted) and bake briefly until it is as dark and crispy as you like.
Carefully remove the skillet from the oven, handling it with plenty of thick cloths. I carry it right to the dining table where it makes a beautiful presentation. While on the table, leave the cloths covering the hot handle. With a large, angled spatula, lift one portion of chicken and mushroom gratinate onto a dinner plate, then spoon over some of the sauce.