Preheat the oven to 275 degrees F. Line a baking sheet with parchment paper.
In a bowl, toss the tomatoes with 1 tablespoon olive oil, salt, and pepper. Place the tomatoes, cut side down, on the prepared baking sheet and drizzle 1 tablespoon water over the tomatoes. Bake in the oven for 1 hour.
Remove from the oven. Carefully peel off the skins and discard. Flip the tomatoes over so they're cut side up, and place back in the oven until the tomatoes are shriveled but not dry, another 30 to 60 minutes. Remove the tomatoes from the oven and allow to cool slightly.
Meanwhile, in a large saucepan, saute the onion in the remaining 1 tablespoon olive oil over low heat until very soft, 10 to 12 minutes. Add the garlic and herbes de provence and cook until fragrant, another 1 to 2 minutes. Add the stock and remaining 1/2 cup water and bring to a simmer. Simmer 15 minutes. Cool slightly.
In a blender, puree the tomatoes (including any cooking liquid on the baking sheet) and the stock mixture until very smooth. You may need to work in batches. Strain through a fine sieve if a very smooth texture is desired. Pour the soup back into the saucepan, season with salt and pepper, and heat gently. To serve, ladle into cups or bowls and top with either a swirl of olive oil or a little sour cream, if desired.