How to Make It
Preheat the oven to 250°. Spread 1/2 tablespoon of the olive oil on a baking sheet. Arrange the tomatoes on the baking sheet and drizzle with the remaining 1/2 tablespoon of olive oil. Season with salt and pepper and top with the thyme sprigs. Bake for about 2 hours, or until the tomatoes are dry and firm but still pliable. Carefully transfer the tomatoes to a plate. Discard the thyme sprigs. Raise the oven temperature to 325°.
Set the garlic heads, cut side up, on a large piece of foil. Spread 2 tablespoons of the butter on the cut sides of the garlic and season with salt and pepper. Seal the garlic in the foil and bake for about 1 hour, or until very soft. Let cool.
Squeeze the garlic from the skins into a mini-processor. Add the remaining 4 tablespoons of butter and process until smooth. Transfer the garlic butter to a bowl and season with salt and pepper.
Spread each Crostini Toast with about 1 teaspoon of the garlic butter, top each with a confit tomato quarter and serve.