Heat a large pot over medium heat. Once hot, add the bacon slices and cook until crispy and golden brown. Remove bacon and let drain on a paper towel. Add onions and peppers to the pot 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 (or before or after or whenever is convenient for you), heat your grill on the highest setting. 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. Serve in bowls topped with the crumbled bacon and shrimp. Store leftovers in the fridge for up to one week.