For the veal: Heat the olive oil in a large saute pan until almost smoking. Sear the chops on both sides until golden brown. Place them in the oven and continue cooking for 5 to 7 minutes for medium doneness. Remove the chops to a plate.
Remove all but 1 tablespoon of the fat from the pan and place over high heat on the stove. Add the shallot and cook until soft. Add the wine and cook until reduced by half. Add the stock and cook until reduced by half. Add the fresh thyme and season with salt and pepper, to taste. Place the chops on a plate and pour the sauce over.
For the peas and carrots: Preheat oven to 375 degrees F.
Melt butter in a medium sauce pan over medium-high heat. Add the carrots and garlic and cook until the carrots are slightly softened. Add the stock and thyme, cover the pan and bring to a simmer. Place the carrots in the oven and cook for 15 minutes. Remove the lid and continue cooking for 10 to 15 minutes, add peas during the last 5 minutes of cooking.
Slice a slit horizontally in the side of each chop. Place 2 slices of fontina, 1 slice of pancetta and a quarter of the mushrooms in each opening. Season each chop on both sides with salt and pepper.
Preheat oven to 400 degrees F.
Slice the mushrooms into 1/4-inch thick slices. Heat the oil in a large saute pan until almost smoking. Add the mushrooms, season with salt and pepper and cook until golden brown. Add the garlic and thyme and continue cooking for 2 minutes. Set aside and let cool.