Combine chicken breasts, parsley, oregano, basil, salt, and pepper in a food processor; process into a smooth paste. Shape chicken mixture into 2 round patties.
Mix bread crumbs and Parmesan cheese together in a shallow bowl. Dredge patties to coat both sides. Arrange on an ungreased baking sheet.
Spread 1 1/2 teaspoon butter over each slice of bread; sprinkle remaining bread crumb-Parmesan mixture on top. Arrange near the chicken patties on the baking sheet.
Bake in the preheated oven until bread is browned, 10 to 15 minutes. Transfer bread to a serving plate. Continue baking chicken until an instant-read thermometer inserted into the center reads 165 degrees F (74 degrees C), 10 to 15 minutes more.
Melt remaining 2 tablespoons butter in a saucepan. Cook and stir onion and garlic in the butter until onion is translucent, about 5 minutes. Add mushrooms and flour; cook and stir until starting to brown, about 5 minutes. Stir in spaghetti sauce; simmer until thickened, 5 to 10 minutes.
Spoon sauce over 2 bread slices. Place a chicken patty in the center; cover with remaining bread slices.