Start 24 charcoal briquettes or pull coals from a good fire.
Slice the breasts on the diagonal to get cutlets with an even thickness. Pound them if needed to get them uniform. Salt and pepper to taste on each of the chicken cutlets.
Put the flour onto a plate and then dredge the cutlets in the flour; set aside on a plate with tin foil. Save the flour for later.
Place the 24 hot coals under your Dutch oven and add 2 Tbsp of olive oil and 2 Tbsp butter.
Once the butter is melted, brown the chicken cutlets, about 4 minutes on the first side and 2 minutes on the second. Don’t overcrowd the oven to ensure good browning. Set cutlets aside on a plate.
When all of the chicken is done, add the bacon (or pancetta) and mushrooms and cook until browned. Then push the mushrooms to one side and add the onions (or shallots) and garlic and cook ~2 more minutes.
Add the wine and chicken broth to the pan and cook until reduced by half.
Add the remaining butter to the oven to melt.
If you still have the flour left, stir 1-2 Tbsp into the cream. Add the cream and Italian seasoning to the oven and cook until thickened.
Add the chicken cutlets back to the oven and nestle into the sauce.
Move 15 of the coals to the Dutch oven lid. Cook until heated through, 10-15 minutes.
Serve over rice or pasta, and garnish with chopped parsley or chives.