Melt butter in a large stockpot or Dutch oven over medium heat. Add garlic, onion, carrots, and celery. Cook, stirring occasionally, until tender, about 3-4 minutes. Stir in cauliflower and bay leaf. Cook, stirring occasionally, until barely crisp-tender, about 3-4 minutes.
Whisk in flour until lightly browned, about 1 minute. Gradually whisk in chicken broth and milk, and cook, whisking constantly until slightly thickened about 3-4 minutes.