Preheat the oven to 425F. Layer a large sheet pan with parchment paper (optional, makes clean-up easier).
Slice the tomatoes into 3-4 pieces. Remove the center stem and core from the tomatoes. Slice the bell peppers into 4-5 wedges, removing the center seeds and stem. Quarter the onions, also removing the core and pulling apart the layers of the onion to make 7-8 pieces total.
Spread the tomatoes, onion pieces, red pepper slices, and cloves of garlic out in an even layer on the sheet pan.
Sprinkle with olive oil, salt, and freshly ground black pepper to taste. Use clean hands or a spatula to toss everything together.
Transfer to the oven to roast on the middle rack at 425F for 30-35 minutes. It is ready when some pieces have char marks (they shouldn't be completely burned, just blackened in spots) and the tomatoes are reduced in size.
Transfer everything to a blender. Be careful not to overfill the blender. Add ½ cup water, vegetable bouillon, basil, and sugar.
Blend on medium speed for 1-2 minutes, until pureed. Vent the blender as needed to avoid steam buildup. Add the remaining ½ cup water as desired (I usually end up adding the full cup of water).
Taste for salt and sugar. Garnish with extra basil and enjoy!
Notes
Tomatoes: Any slicing tomato should work fine, just make sure to remove the core. I have made this recipe with half cherry tomatoes/half slicing tomatoes with success, though it yields a slightly less uniform texture.
Water/bouillon: 1 cup of vegetable broth can be used in place of the water and bouillon.
Freezing: This tomato soup freezes well. If freezing in a glass jar, make sure to let the soup cool to room temp before freezing and leave at least one inch of space at the top of the jar. Let thaw overnight in the fridge when ready to reheat.