Preheat oven to 250°F. Arrange cherry tomatoes in a single layer in a 9-by-13-inch glass or ceramic baking dish. Top with thyme sprigs, garlic and shallot; season with salt and pepper. Drizzle with extra virgin coconut oil and stir to combine.
Bake, stirring occasionally, until tomatoes pop and ooze, 2 1/2 to 3 hours. Remove baking dish from the oven and discard thyme sprigs. Use immediately or let cool and transfer to a covered container. Refrigerate until ready to use. Tomatoes will keep for 3 days.