Step 1

Heat broiler. Halve large tomatoes crosswise (through the equator). Starting with cut sides, grate tomatoes on the large holes of a box grater into a medium bowl; discard or compost skins. Add beans and season generously with salt and pepper.

Step 2

Heat 3 Tbsp. oil in a large ovenproof skillet over medium-high. Add cherry tomatoes; cook, shaking pan occasionally, until browned in spots, about 3 minutes. Add garlic; cook, stirring, until fragrant, about 1 minute.

Step 3

Stir in grated tomato mixture and reserved basil stems. Cook, stirring occasionally, until mixture is thickened and flavorful, 10–15 minutes. Taste and season with salt and pepper.

Step 4

Remove basil stems from pan; stir in ¼ cup basil leaves. Shake skillet to evenly distribute beans. Top with mozzarella and 2 Tbsp. Parmesan. Broil until cheese is melted and browned in spots, about 3 minutes.

Step 5

Spoon tomato beans over toast as desired. Top with more basil leaves and Parmesan and drizzle with oil. Season generously with more pepper.