Preheat the broiler to high with a rack set 2 inches from the heat source. Line a plate with a paper towel.
Heat a large skillet over medium-high heat. When hot, pour in the oil. Add half of the kielbasa rounds and cook until browned, about 2 minutes. Flip and cook for 1 minute more. Transfer to the lined plate. Cook the remaining rounds until both sides are browned and add to the plate. Reduce the heat to medium, add the onion, and cook until softened and slightly browned, about 5 minutes.
Whisk the tomato paste, brown sugar, vinegar and chipotle into the onion. Pour half a can of beans (including the bean liquid) into the skillet and mash with a fork until creamy. Add the rest of the beans, the kielbasa, 1/2 cup water, 1 teaspoon salt and a couple turns of pepper. Simmer until thick and creamy, about 20 minutes.
Meanwhile, toss the hot dog bun cubes with the melted butter on a baking sheet and sprinkle with salt and pepper. Broil until toasted and browned, flipping occasionally, about 2 minutes.
Divide the kielbasa and beans among 4 bowls. Top evenly with the hot dog bun croutons and pickle relish.