Cook the pasta in a large pot of boiling, salted water until it's very aldente -- it will finish cooking with the sauce later. Add ½ cup of the pasta water to a small bowl and set is aside. Then, drain the pasta, toss with a bit of olive oil, cover, and set that aside, too. Remove the stems and all of the seeds from 3 of the roasted and peeled peppers. Add them to a food processor fitted with the blade attachment, or a blender, and purée them until they are as smooth as possible. Set aside. Remove the stem and seeds from the last roasted and peeled pepper, and cut it into thin slices. Set aside.
Coat the bottom of a large sauté pan with about 1 tablespoon of the olive oil, and place it over medium-low heat. Add the garlic and let it become slightly golden, about 4 minutes.
Add the oregano, puréed peppers, sliced peppers, olives, tomato, and sardines. Cook over low heat for about 20 minutes.
Add the ½ cup pasta water, spinach, the remaining 3 tablespoons of olive oil, salt, sugar and the cooked pasta. Gently stir to coat all of the pasta and evenly distribute the sauce.
Create 4 small openings in the pasta, with a few inches between them. Crack 1 egg into each opening. Sprinkle the eggs with a bit of salt and the chili flakes.
Cover with a fitted lid or foil, turn the heat to low, and simmer until the eggs are cooked the way you like them. For a soft yolk, it's about 10 minutes.