Heat a large pot over medium heat. Add onions and peppers with a sprinkle of salt and pepper and cook for 5 minutes, stirring occasionally. Add garlic and cook for an additional minute. Whisk in the flour, cooking for 1-2 minutes or until flour becomes golden in color and smells a bit nutty. Add chicken stock, potatoes, and corn. Bring to a boil then reduce to a simmer and cook for 10-15 minutes.
While soup is simmering season shrimp with salt and pepper, brush with a thin layer or barbecue sauce, then cook for 2-3 minutes per side. Remove from grill and toss with remaining barbecue sauce.
Once soup has slightly thickened and the potatoes have started to break down, stir in milk and cream. Add 1/4 teaspoon of pepper, then season according to your tastes.
