Saute the onion and carrot. Preheat the oven to 375F. Heat the oil in a 12-inch skillet over medium-high heat. Add the onion and carrot, and saute for 4 to 5 minutes, until softened. Add the garlic and saute another minute.
Add more veggies and simmer. Add the crushed tomatoes, roasted red peppers, herbs de Provence, salt, and pepper. Reduce the heat to low, cover and simmer for 10 minutes.
Slice the vegetables. While the sauce is simmering, use a mandoline to thinly slice the eggplant, zucchini, yellow squash, and tomatoes.
Blend the sauce. Transfer the simmered vegetables to a blender and pulse until lightly blended. Alternatively, transfer to a 4-cup measuring cup and use an immersion blender to lightly puree it. Then pour it back into the skillet and spread into a flat layer.
Arrange the vegetables. Alternate the sliced vegetables, placing them in a circular pattern around the outside of the skillet, working towards the center.
Drizzle the dressing. In a small bowl, stir together the olive oil, herbs, garlic, salt, and pepper. Then drizzle it on top of the vegetables.
Bake. Cover the pan with a lid or aluminum foil and bake for 40 minutes. Remove the lid and bake another 20 minutes, until the vegetables are tender and the top is lightly golden.
Serve. Garnish the skillet with a few sprigs of fresh thyme leaves before serving, or plate a portion of ratatouille with a few spoonfuls of sauce. If you'd like to see how I plate it like the movie, watch my tutorial video above!