Heat a medium nonstick skillet over medium-high heat. Add oil to pan; swirl to coat. Add onion and minced garlic to pan; sauté 4 minutes. Add tomato paste; cook 1 minute, stirring constantly. Add wine; cook 1 minute or until liquid almost evaporates. Add sugar, salt, peppers, and tomatoes. Cover and reduce heat to medium; simmer 2 minutes. Crack eggs, 1 at a time, on top of tomato mixture. Cover and cook 5 minutes or until whites are set and yolks are soft.
Place bread slices on a baking sheet; broil 1 1/2 minutes on each side or until toasted. Rub bread with halved garlic clove. Sprinkle 2 tablespoons cheese on each bread slice; broil 1 1/2 minutes or until cheese melts. Divide tomato mixture and eggs evenly among 4 shallow bowls. Serve with garlic toasts.