Preheat oven to 375 degrees F.
Pour tomato puree into bottom of an oval baking dish, approximately 10 inches across the long way. Drop the sliced garlic cloves and chopped onion into the sauce, stir in one tablespoon of the olive oil and season the sauce generously with salt and pepper.
Drizzle the remaining tablespoon olive oil over the vegetables and season them generously with salt and pepper. Remove the leaves from the thyme sprigs with your fingertips, running them down the stem. Sprinkle the fresh thyme over the dish.
Bake for approximately 45 to 55 minutes, until vegetables have released their liquid and are clearly cooked, but with some structure left so they are not totally limp. They should not be brown at the edges, and you should see that the tomato sauce is bubbling up around them.