Cut broccoli florets into small pieces and reserve. Dice the stems into pieces.
Place bacon in a stockpot and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain bacon slices on paper towels and reserve the grease in the pot.
Cook broccoli stems, carrots, celery, onion, and coconut oil in the pot over medium heat until softened, about 10 minutes. Add garlic and cook until fragrant, about 1 minute. Add flour; stir for 2 minutes. Pour in stock, beans, mustard, salt, cayenne, and black pepper. Reduce heat to a simmer; cook until flavors blend, about 10 minutes.
Fill blender halfway with the soup. Cover and hold lid down with a potholder; pulse a few times before leaving on to blend until smooth. Pour into another pot. Repeat with remaining soup. Add the reserved broccoli florets and simmer until tender, about 5 minutes. Dice the bacon and sprinkle over soup.