Heat oven to 375 degrees. Drain tomatoes and reserve liquid. Halve them and put in a roasting pan; sprinkle with 2 tablespoons oil and the thyme, if using. Roast, turning once or twice, until lightly browned, about 30 minutes. Use wooden spoon to scrape up browned bits from pan, adding a little liquid if necessary.
Put remaining olive oil in a deep skillet or medium saucepan over medium-high heat. When it's hot, add garlic and cook just until it begins to color, a minute or so. Add carrot and onion and cook, sprinkling with salt and pepper and stirring, for about 5 minutes. Stir in stock or water, along with contents of roasting pan and reserved tomato juice.
Turn heat to high and bring soup to a boil, then lower heat so it bubbles gently. Cover and cook until vegetables are very tender, 20 to 30 minutes. Garnish with parsley and serve.