Preheat the oven to 375 degrees F. Butter 4 (5-inch) oven-safe ramekins or earthenware dishes.
In a medium skillet, heat the olive oil over medium-high heat. Add the shallot, and garlic and saute until fragrant. Stir in the crushed red pepper flakes, tomatoes, and tomato paste and cook until thickened, about 5 minutes. Season with salt and pepper, to taste, and fold in the basil.
Fill the prepared ramekins with the tomato mixture. Top each with a cracked egg. Put the ramekins on a baking sheet and bake until the eggs are set, about 12 to 15 minutes. Remove the ramekins from the oven, garnish with basil and serve.