Combine the olive oil, tomatoes, garlic, peppers, paprika, salt, and 2 cups of water in a large skillet or braiser.

Bring to a simmer over medium-high heat, then lower to the lowest possible flame and cook for 4-5 hours. This may require moving your skillet to the smallest burner on the stove. Stir occasionally and add water, 1 cup at a time, as necessary until a deeply flavorful, thick, jammy base forms.

To finish, gently crack the eggs over the sauce. Cover and cook on medium-high heat until the whites are hardened but the yolk is still runny, about 5 minutes. Serve immediately with homemade bread.

Sauce can be frozen or stored in the refrigerator for up to 5 days.