Heat broiler to high and place red peppers, cut side down, on a baking sheet about 4 inches from the broiler. Broil until skins are mostly blackened, checking frequently, about 5-7 minutes. Place in a sealed container and let steam for 20 minutes. Peel off skins and dice peppers.
Meanwhile, heat oven to 400 degrees. Toss cauliflower in 1 Tbsp. olive oil and spread evenly on a baking sheet. Roast 20-30 minutes, stirring once halfway through.
Heat the other 1 Tbsp. in a stock pot over medium heat and saute the onion until tender, about 5-7 minutes. Add the garlic, thyme, and red pepper flakes and cook about 1 minute. Add diced red peppers, roasted cauliflower, broth, paprika, and goat cheese and simmer 10 minutes.
Puree to desired consistency with an immersion blender, stir in lemon juice, season with salt and pepper, and serve.