Preheat the broiler on high (500°F). Position an oven rack 6 inches below the heating element (not directly below).
Cut the tomatoes in half. Cut a tiny sliver from the bottom of each half so that the tomatoes can stand upright without wobbling.
Spray the tomatoes all over with olive oil. Place them on a broiler-safe rimmed baking dish, cut side up.
Sprinkle the tomatoes with salt, pepper, garlic powder, and thyme. Top with Parmesan, 2 tablespoons for each tomato half.
Broil until the cheese is golden brown, 3-5 minutes. Serve immediately.
Video
Notes
Keep a close eye on the tomatoes while they're in the oven. Even when not directly under the heating element, they can burn quite easily. Broiling is always challenging in this way, and this recipe is no different.
If you prefer an oil with a high smoke point, you can use avocado oil. Another tasty option is to use melted butter.
Shredded cheddar is also good in this recipe.
There's no need to peel the tomatoes.
You can keep the leftovers in an airtight container in the fridge for 3-4 days and gently reheat them in the microwave at 50% power or in a 350°F oven. I don't recommend freezing the leftovers.