Heat 2 tablespoons (30 ml) of olive oil in a large frying pan over medium heat. Add the garlic and red chili pepper flakes and cook for 30 seconds. Stir in the tomatoes and their juices, the sprigs of thyme, a couple of basil leaves, the oregano and the pinch of sugar. Break the tomatoes into pieces with a wooden spoon and cook, letting the sauce bubble, for about 13 to 15 minutes over medium-low heat.
Use a spoon to make 4 small wells in the tomato sauce and crack an egg into each well. Season the eggs with sea salt and black pepper to taste. Cover the pan with a lid and continue to cook over medium-low heat until the eggs are set, about 2 to 3 minutes for soft runny yolks.
While the eggs cook, heat a large grilling pan over medium-high heat and brush the bread slices with the remaining extra-virgin olive oil. Grill the bread until crispy on both sides, about 2 minutes. Remove the eggs in purgatory from the heat. Sprinkle the remaining basil leaves on top, season with extra black pepper if desired and serve with the grilled bread.