Preheat oven to 300 degrees F and line two baking sheets with parchment paper.

In a large bowl, combine halved tomatoes, olive oil, salt, and pepper.

Arrange the tomatoes cut-side up on the prepared baking sheets.

Scatter garlic cloves and thyme pieces over the tomatoes.

Bake for 4 hours and 30 minutes, or until the tomatoes have collapsed and begun to brown, rotating pans halfway through.

Cool the tomatoes on parchment paper on a wire rack.

Transfer cooled tomatoes to sealable plastic bags for short-term storage (up to one week).

For longer storage, transfer tomatoes to a jar with a tight-fitting lid and cover them with oil by 1/4 inch.

Cover and store in the refrigerator for up to 1 month.