Heat oven to 400 degrees. On a rimmed baking sheet, toss tomatoes and garlic with oil and thyme and season with salt and pepper. Roast until caramelized, about 30 minutes, then transfer tomatoes and juices to a straight-sided 9-inch-round (2-inch-deep) baking dish and let cool slightly. Decrease oven temperature to 350 degrees.
In a medium bowl, whisk together eggs, cornstarch, coconut milk, cheese, 1/2 teaspoon salt, and herbs, then pour mixture over tomatoes.
Bake until top is golden brown and edges are puffed, 35 to 40 minutes. Serve warm or at room temperature.
Basque-ing in Flavor
Coconut milk lends this elegant but easy clafoutis (think frittata meets souffle) an uncommon richness.