Preheat the oven to 425˚F.

Line a large heavy-duty rimmed sheet pan with a piece of parchment paper. (I like to cover the sheet pan with aluminum foil, first, for easier clean up, but it’s not necessary.)

Cut each tomato in half length wise, and, leaving in the core, scrape out the seeds and ribs with a tomato shark or a serrated spoon.

Brush 1 tablespoon of the olive oil over the parchment.

Arrange the tomato halves, cut side up, on the parchment.

Season the cavity of each tomato half with a pinch of salt, a good pinch of sugar, and some of the thyme leaves. Drizzle a few drops of balsamic vinegar inside each tomato half. (An easy way to do this is to pour some vinegar into a small bowl and use a ⅛ teaspoon measure to distribute it. Or just hold your thumb over the vinegar bottle opening to dispense drops!)

Drop a slice or two of garlic in each half , and pour 1 teaspoon of the olive oil into each half. It will look like a lot of olive; that’s okay.

Roast the tomatoes until they collapse and are brown around the edges, the garlic is browned, and the juices are somewhat caramelized on the sheet pan, 30 to 40 minutes. (At this temperature, you can roast them up to about 55 minutes before the bottoms get too dark. Some of the really hefty—and underripe—plum tomatoes may want to go this long to be tastiest.)

Let the tomatoes cool for a few minutes on the sheet pan. Carefully transfer them to a serving plate. (If the juices are very caramelized, the tomatoes may stick a bit; take care not to rip the skin.)

Serve warm or at room temperature. They will also keep in the fridge for about a week.