Set the oven to broil and move a rack to the highest position.
Arrange whole bell peppers and halved tomatoes on a rimmed baking sheet. (If using cherry tomatoes, add them about halfway through cooking instead).
Broil for about 10-15 minutes until the pepper skins get a nice char and the tomatoes soften considerably, rotating the peppers every few minutes to cook all sides.
Remove from oven and place peppers into a medium bowl. Cover with a plate and let them steam for 15 minutes.
Meanwhile, in a food processor, first pulse garlic cloves a few times to roughly chop them.
Add the tomatoes, salt, and red wine vinegar and pulse a few more times.
When the peppers are done steaming, carefully remove the tops and seeds, and slip off the skin with a paper towel. You may want to rinse them under cold water first to cool them down.
Add all peppers to the food processor and pulse a few times. Slowly add the olive oil as you continue to pulse, and it will turn to a chunky sauce consistency.
Add the paprikas and salt, pulse a few more times. Taste and adjust for seasoning, then serve with fish, chicken, pasta, vegetables, or almost anything else!