Heat a large stockpot over medium heat. Add bacon and cook until brown and crispy, about 6-8 minutes. Transfer to a paper towel-lined plate to drain and set aside.
Melt the butter in the stockpot. Add onion, carrots, and celery. Cook, stirring occasionally, until tender, about 3-4 minutes. Add garlic and cook for another minute. Stir in flour and cook until lightly browned, about 1 minute. Stir in paprika and add bay leaf.
Pour in broth and milk. Bring to a boil, then reduce heat to a simmer, stirring until thickened, about 6-8 minutes.
Meanwhile, steam broccoli and cauliflower in the microwave according to package directions. Roughly chop and stir into chowder.
Stir in bacon, reserving some for garnish. Discard bay leaf.
Transfer to bowls and garnish with reserved bacon.