Preheat oven to 350°F. Toss tomatoes and garlic with oil in a roasting pan and season with salt and pepper. Arrange tomatoes cut side up and roast for 15 minutes. Turn tomatoes over and roast until soft, another 20 minutes. Let cool, then scrape mixture into a blender, add oregano and red pepper flakes, and puree until smooth.
Place 4 shallow ovenproof bowls on a baking sheet. Strain pureed sauce into bowls, pressing on solids. Crack 2 eggs into each bowl and season with salt and pepper. Sprinkle cheese over eggs and bake until whites are just set, about 15 minutes. Serve hot.
