Heat oven to 400 degrees. Slice the top third off tomatoes and use a small spoon to remove core and seeds. Arrange in a baking dish, drizzle with oil, and season with salt and pepper. Sprinkle with thyme and garlic. Roast until tomatoes are tender and caramelized, about 30 minutes.
Crack an egg into each tomato and season with salt and pepper. Bake until eggs are just set, 7 to 9 minutes more.
For better aim, crack the egg into a teacup first, then pour it on the tomato.