Heat a large Dutch oven over medium-high. Add olive oil, then the diced onion, red pepper, yellow pepper, and jalapeño. Cook for about 8 to 10 minutes until the vegetables soften.
Add minced garlic and cook 1 to 2 minutes more, stirring to avoid burning.
Reduce heat to medium. Add smoked paprika, cumin, chili flakes, salt, black pepper, and chili powder. Stir to coat the vegetables and toast the spices for 1 minute. Add tomato paste and stir until well combined.
Pour in crushed tomatoes, diced tomatoes, vegetable stock, BBQ sauce, Worcestershire sauce, and brown sugar (if using). Stir to combine, then add in beans.
Add in the beans, and bring to a boil. Lower heat to medium-low and simmer for 50 to 60 minutes, stirring occasionally, until the chili thickens and the flavor deepens.
Taste and adjust salt, sweetness, or heat as needed. If you want more smoky BBQ character, stir in a little extra BBQ sauce before serving.
Serve topped with chopped scallions, sour cream, shredded cheese, or pickled jalapeño peppers, as desired.