1. In a large ovenproof skillet over medium heat, warm oil. Add chicken gizzards and necks along with ½ teaspoon each of salt and pepper. Arrange in a single layer and cook until browned on one side, 6 to 8 minutes. Stir in onions and bell pepper. Cook, stirring often, until onions begin to brown, 10 to 12 minutes. Remove from the heat, and stir in stock and wine. Return the skillet to stovetop and bring to a simmer. Add bay leaves and red pepper flakes. Cook, stirring, until the liquid is reduced by half, about 10 minutes. Cover, reduce heat to low, and simmer until gizzards are tender, about 45 minutes.
2. Remove and set aside the gizzards and necks; keep warm. Add tomatoes to the skillet; stir to combine. Cook, stirring often, until tomatoes are softened, about 10 minutes. Stir in tomato paste and simmer 5 minutes. Stir in nutmeg and the remaining 2½ teaspoons salt and ½ teaspoon black pepper. Remove from heat and let stand 10 minutes. Discard bay leaves.
3. Preheat oven to 375 degrees. Return skillet to heat and bring to a simmer. Make 4 wells in the tomato mixture and crack an egg into each well. Bake until egg whites are set, about 10 minutes. Let stand 2 minutes before serving. Serve with treserved chicken gizzards and necks.