Preheat oven to 180˚C (350˚F). Line a baking sheet with parchment paper. In a bowl, mix flour, salt and pepper. In a second bowl, fork-beat eggs and milk. In a third bowl, mix breadcrumbs, Parmesan and oregano. Dip all sides of chicken breasts in the flour mixture; shaking off excess. Roll in egg mixture to moisten flour coating; letting excess egg drip off. Dredge in breadcrumb mixture; coating all sides.
Drizzle 2 tbsp (30 mL) olive oil on lined baking sheet; place chicken breasts overtop. Bake 10 min. Flip over; bake another 10 min., until breading is golden and internal temperature of chicken reaches 74˚C (165˚F). Remove from oven (but keep oven on).
Meanwhile, in a saucepan, heat rest of oil on medium-low heat. Stir in carrot, onion and garlic; cook to soften but do not brown. Stir in tomatoes and sugar. Lower heat to a gentle simmer; cook until sauce has thickened, about 15 min. Stir in basil and parsley. Season with salt and pepper, if desired.
Spoon about ¼ cup (60 mL) tomato sauce on top of each chicken breast; top with a slice of provolone. Bake another 5 min., or until cheese is melted. Serve with Caesar Salad, if desired.