Preheat the oven to 400º.
Place the peppers and onion into a roasting pan or oven safe skillet and drizzle them with 1 tablespoon of olive oil. Toss to coat.
Cut the top off of garlic bulb, exposing the tops of the cloves. Remove one clove, mince it, and reserve it for later.
Set the garlic bulb on a sheet of foil and drizzle it with 1 tablespoon of olive oil. Loosely wrap it in foil.
Place the onions, peppers and garlic into the oven.
Bake the onions and peppers until browned in spots and some blisters appear on the peppers, 30-35 minutes, flipping once or twice during baking.
Bake the garlic until cloves are light golden brown, about 35-40 minutes. Remove it from oven, open up the foil and allow it to cool.
When the garlic is cool enough to handle, squeeze the bulb to extract the roasted cloves from their skins.
Blend the veggies. Transfer the peppers, onions, tomatoes, roasted garlic and raw garlic to a food processor or blender, or place them in a large pot and blend with an immersion blender. You can add some broth to help this along if needed.
If you used a food processor or blender, transfer the mixture to a large pot now. Stir in the broth, vinegar, paprika and thyme, and place the pot over medium heat.
Bring the mixture to a simmer, lower heat and allow to simmer for about 10 minutes, until it thickens up a bit.
Remove the pot from heat and season with salt and pepper to taste.