Cut the tops off of the tomatoes approximately 1/4 inch down. Scoop out the insides of the tomatoes (I found this easiest with a melon baller, but you can also use a spoon).
Sprinkle the inside of each tomato with salt. Place the tomatoes upside down to drain on top of paper towels on a plate. Let them sit for 30 minutes. (This is an important step because it will remove extra moisture, preventing the tomatoes from being soggy later on).
Meanwhile, make the ratatouille filling. Chop the eggplant, zucchini, and yellow squash into 1/4-1/2" pieces. Heat the olive oil in a large skillet over medium heat. When hot, add the eggplant, zucchini, squash, and onion. Cool until tender, approximately 7 minutes.
Add the garlic, dried thyme, salt, and pepper. Stir and cook until fragrant, approximately 1 minute. Take off the heat and set aside until the tomatoes are done draining.
When the tomatoes have been draining for 30 minutes, use a paper towel to dab the inside of each tomato dry. Stuff each tomato with the ratatouille mixture. Place the tomatoes in a baking dish.
Bake the tomatoes for 20-25 minutes until the tops are starting to slightly golden. Serve immediately with your favorite sides.