Preheat the oven to 275 degrees.
Roughly chop the fresh thyme leaves. Place a cooling rack on a sheet pan. Place the tomatoes cut-side up on the rack. Drizzle with olive oil and sprinkle with salt, pepper and the fresh thyme. Roast approximately 1 hour 30 minutes, or until the tomatoes are very soft and slightly shrunken. Set aside.
Increase the oven temperature to 400 degrees. Place the baguette slices on a baking sheet, drizzle with olive oil and bake until lightly golden brown, about 10 minutes (watch carefully so as not to overcook). Rub the crostino with garlic clove and top each with a roasted tomato. Garnish with a little of the grated Parmesan cheese.
Note: the tomatoes can be roasted ahead of time and stored in the refrigerator. When ready to serve, warm them for a few minutes in the oven with the baguette slices.