1/2 cup plus 2 tablespoons extra-virgin olive oil
1 large head romaine (about 1 1/2 lb)
1 large garlic clove
1/4 cup loosely packed fresh flat-leaf parsley leaves
1/2 teaspoon salt
3/8 teaspoon black pepper
1 oz finely grated parmesan (1/2 cup), plus additional for serving
6 large tomatoes (about 3 inches in diameter)
6 large eggs at room temperature
Strip romaine leaves from stems, reserving both separately, then tear leaves into roughly 2-inch pieces. Measure 4 loosely packed cups of leaves and reserve remainder. With motor running, add garlic to food processor to finely chop. Turn off and add the 4 cups romaine leaves along with the parsley, 1/4 teaspoon salt, 1/4 teaspoon pepper, and cheese, then pulse until finely chopped. With motor running, add remaining cup oil in a slow stream, blending until incorporated.
Put oven rack in upper third of oven and preheat oven to 400°F.
Cut off about 1/8 inch from top of each tomato with a sharp knife. Gently scrape out pulp and seeds with a spoon and discard them. Put tomatoes, cut sides up, in a 9-inch glass or ceramic dish and spoon 1 tablespoon romaine-parsley pesto into each tomato (you will have extra pesto). Crack 1 egg into each tomato and season with salt and pepper. Bake eggs in tomatoes until whites are set and yolks are still runny, 18 to 22 minutes.