Place the chopped bacon into a large pot over medium heat. Cook until crispy and golden brown, stirring occasionally so it cooks evenly. Remove the bacon and place it on a paper towel-lined plate, leaving a little bacon grease in the pot for flavor.
Add butter to the same pot with the bacon grease. Stir in the diced onion, bell pepper, and jalapeño, then cook for about 5 minutes until softened. Add the garlic and cook for another 30 seconds until fragrant.
Sprinkle the flour over the vegetables and stir well so everything is coated evenly. Let the flour cook briefly to remove the raw taste. Slowly pour in the chicken broth while stirring continuously to create a smooth broth.
Pour in the milk and heavy cream, then stir until combined. Add the potatoes, corn, smoked paprika, mustard powder, salt, and black pepper. The mixture will already start smelling rich and comforting at this stage.
Place the chicken directly into the soup and bring everything to a gentle boil. Lower the heat and let it simmer until the potatoes are tender and the chicken is fully cooked. This usually takes around 15 to 20 minutes.
Remove the cooked chicken and shred it using two forks. Use an immersion blender to blend about half of the soup for a creamy texture while keeping some chunky pieces. Return the shredded chicken back into the pot.
Taste the chowder and adjust seasoning if needed. Ladle the soup into bowls and top with crispy bacon, green onions, and shredded cheese. Serve hot with crackers or warm bread on the side.