Heat a Dutch oven over medium heat; line a plate with a paper towel. Add the bacon to the pot and cook, stirring occasionally, until crisp, 5 to 7 minutes. With a slotted spoon, transfer the bacon to the lined plate to drain.
Discard most of the bacon fat, leaving about 2 tablespoons in the pot. Return to medium heat, add the onion, bell pepper and garlic and saute until beginning to brown, about 3 minutes. Add the brown sugar, coffee, ketchup, mustard, chile paste and 1 teaspoon each salt and pepper, then add the beans and stir to combine. Bring to a simmer, then cover and cook until the sauce has thickened, 12 to 15 minutes.
Remove the pot from the heat and stir in the sour cream. Taste and adjust the seasoning as needed. Transfer the dip to a serving bowl and garnish with the Cheddar, green onions and reserved bacon. Serve with crackers or chips alongside.