For the sauce, in a food processor, puree all ingredients. Season with salt.
For the eggs, in a large skillet, heat the EVOO over medium-high. Add the bell pepper and jalapenos. Cook, stirring, until softened, about 3 minutes. Add the garlic and spices; cook, stirring, about 2 minutes. Add the tomatoes and their liquid. Cook, stirring occasionally, about 5 minutes. Season with salt and pepper.
Using the back of a spoon, make 6 evenly spaced indentations in the sauce. Crack 1 egg into each; season. Reduce the heat to medium-low. Cover and cook until the whites are just set, about 7 minutes. Serve with the pita and garlic-herb hot sauce.