Preheat the oven to 400 degrees F (200 degrees C).
Mix carrots, red bell peppers, onion, garlic, paprika, cumin, salt, and pepper together in a bowl. Transfer to a rimmed baking sheet. Drizzle olive oil on top and toss.
Roast in the preheated oven until tender, about 30 minutes.
Bring vegetable broth, bay leaf, and oregano to a boil in a soup pot. Add roasted vegetables to the pot. Remove bay leaf and add red pepper. Simmer for 15 minutes.
Blend soup with an immersion blender.
Add apple cider vinegar to pureed soup. Serve with hot sauce.