Slice tops and bottoms off bell peppers and finely dice. Remove and discard seeds and membranes. Slice each pepper into four 1/2-inch-thick rings.

Combine the diced pepper with avocado, onion, jalapeño, cilantro, tomatoes, lime juice, and 1/2 teaspoon salt in a medium bowl.

Heat 1 teaspoon oil in a large nonstick skillet over medium heat. Add 4 bell pepper rings, then crack 1 egg into the middle of each ring. Season with 1/8 teaspoon each salt and pepper. Cook until the whites are mostly set but the yolks are still runny, 2 to 3 minutes. Gently flip and cook 1 minute more for runny yolks, 1 1/2 to 2 minutes more for firmer yolks. Transfer to serving plates and repeat with the remaining pepper rings and eggs.

Serve with the avocado salsa and garnish with additional cilantro, if desired.