Melt butter in a saucepan over medium heat. Stir in garlic and onion, and cook until the onion has softened and turned translucent, about 2 minutes. Pour in diced tomatoes and sugar. Increase heat to medium-high, and bring to a simmer, then reduce heat to medium-low, and continue simmering for 10 minutes, stirring occasionally. Once the sauce has simmered, stir in the cream and season to taste with salt and pepper. Simmer for an additional 3 minutes. Lower heat and keep sauce warm.
Stir together breadcrumbs, 2 tablespoons Parmesan cheese, and dried oregano; set aside. In a small bowl, whisk together egg and 2 tablespoons milk until blended. Dip chicken breasts into the egg, then press into breadcrumb mixture to coat both sides, shaking off excess.
Heat olive oil in a large frypan over medium heat. Add chicken breasts and cook on both sides until the juices run clear and the breadcrumbs are golden brown, about 10 minutes.
To serve, spoon sauce over chicken and top with mozzarella and parmesan cheeses. Let stand a few minutes until the cheese has melted from the heat of the sauce.