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 bread crumbs, 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 skillet over medium heat. Add chicken breasts and cook on both sides until they reach an internal temperature of 160°F (70°C), and the bread crumb crust is golden brown, about 10 minutes.