Preheat oven to 275 F degrees. Line a small baking sheet with parchment paper or use a 13 x 9 baking dish. If you want to make more tomatoes, use a large baking sheet.
Arrange the tomato halves, cut side up, in one layer on the prepared baking sheet.
Place a sliver of garlic on top of each tomato and scatter the thyme sprigs over. Drizzle a little oil over the tomatoes and sprinkle with a pinch of salt. Bake until desired texture is reached. I like to go 3 hours. More time will result in drier tomatoes. Less time will result in juicier tomatoes. Ovens also vary, so check tomatoes periodically.
Store in the refrigerator in a covered container for up to a week. Covered in oil, the tomatoes will last a few weeks. You can also freeze them right on the sheet pan and when the tomatoes are frozen, transfer them to a covered container to freeze (ideally a freezer bag that is as small as will fit the tomatoes.)
Notes
*You can also use halved cherry or grape tomatoes and cook for less time.