Preheat your oven to 400℉. Line a baking sheet or sheet pan with parchment paper for easy clean up. Spray with cooking spray. Rough chop red bell peppers, tomatoes, carrots, and onion. Cut the top end off a bulb of garlic. Note: you can peel your carrot if you want to but there is no need to.
Place the red bell peppers (skin side up), tomatoes, carrots, onion, and bulb of garlic on the prepared baking sheet. Drizzle the olive oil, oregano, thyme, smoked paprika, red pepper flakes, salt, & pepper on top. Give them a toss to make sure everything is coated.
Roast in the preheated oven for 35-45 minutes. Oven times will vary. When the vegetables are done roasting, the red bell pepper will have charred skins. You want this to add depth of flavor to the soup.
Add the roasted vegetables except the garlic to a high-speed blender. To add the garlic cloves, carefully squeeze them out of the skin being careful not to get the skins in the blender. Add 3 cups of the chicken broth and gouda. Blend everything until smooth, pushing down the sides as needed with a rubber spatula.
To heat the soup, pour it into a large stockpot and heat on medium heat until it starts to bubble. Then lower to medium-low or low heat for another minute or two. If it's too thick, add 1 more cup of broth or a little water. Give it a taste and add additional salt as needed. *careful when handling hot liquid.
Hint: if you don't have a high-speed blender, you can add the soup ingredients including the roasted vegetables, broth, and Gouda cheese to a large pot and use an immersion blender to blend it.