Set an oven rack in the center position and preheat the oven to 350°F (175°C). Chop the yellow onion and green bell pepper, mince the garlic, and cut the thick bacon into 1/4-inch sections. Drain and rinse the pinto, kidney, and cannellini beans, then set them aside until needed.
Place the sliced bacon in a large Dutch oven over medium heat. Cook for approximately 7–10 minutes, stirring from time to time, until the pieces are browned and crisp.
Using a slotted spoon, transfer the cooked bacon to a plate lined with paper towels. Carefully remove the excess bacon drippings from the Dutch oven, leaving approximately 1 tablespoon of rendered fat in the pot.
Add the chopped onion and green bell pepper to the reserved bacon fat. Continue cooking over medium heat for about 5–7 minutes, stirring occasionally, until the vegetables become tender.
Add the minced garlic, chili powder, and optional cayenne pepper. Stir and cook for approximately 1 minute, just until the garlic and spices become fragrant.
Place the ground beef in the Dutch oven with the cooked vegetables. Season with the kosher salt and black pepper.
Cook for approximately 4–5 minutes, breaking the beef into smaller pieces with a wooden spoon as it cooks. Continue until the meat is fully cooked and evenly browned.
Add the drained pinto beans, kidney beans, and cannellini beans to the Dutch oven. Return the cooked bacon to the mixture.
Pour in the water, barbecue sauce, ketchup, and Dijon mustard, then add the packed brown sugar. Stir thoroughly so the meat, beans, vegetables, and sauce ingredients are evenly combined.
Bring the mixture to a gentle simmer over medium heat.
Cover the Dutch oven and transfer it to the preheated oven. Bake for approximately 45 minutes, allowing the sauce to thicken and the ingredients to meld together.
For a thicker consistency and a lightly caramelized surface, the lid may be removed during the final 10 minutes of baking.
Carefully take the Dutch oven out of the oven. Taste the beans and add a little additional salt only if necessary.
Serve the Cowboy Beans hot.