Preheat oven to 350 degrees. Set four 12-ounce ovenproof bowls or ramekins on a large rimmed baking sheet.
In a large saucepan, heat oil over medium. Add garlic and rosemary; cook, stirring, until garlic is golden, about 2 minutes. Add diced tomatoes (with juice), crushed tomatoes, and 2 tablespoons Parmesan; bring to a boil. Reduce to a simmer, and cook, stirring occasionally, until slightly thickened, 2 to 4 minutes. Season tomato sauce with salt and pepper.
Divide tomato sauce among bowls, reserving 1 cup. Crack 2 eggs into each bowl. Dividing evenly, top with reserved sauce and 2 tablespoons Parmesan. Bake until egg whites are just opaque (yolks should still be soft), 24 to 28 minutes, rotating sheet halfway through.
A rimmed baking sheet helps you transfer the baking dishes in and out of the oven.