Chop the cauliflower into florets, dice carrots and celery, chop the onion, and mince the garlic. Cook and crumble bacon; set aside.

Measure out broth, milk/cream, cheese, breadcrumbs, and butter so everything is ready.

In a large pot over medium heat, melt 1 tablespoon of butter. Add onion, carrot, and celery. Cook for 5–7 minutes until softened and aromatic. Add garlic and cook for 30 seconds.

Add the chopped cauliflower and pour in the 4 cups of broth. Bring to a boil, then reduce to a simmer. Cook for 12–15 minutes, until the cauliflower is very tender.

Remove the pot from heat. Use an immersion blender to puree until smooth, or transfer in batches to a blender.

Return the blended soup to low heat. Gradually stir in milk or cream to warm it through. Ladle a small amount of hot soup into the cheese to temper it, then stir the tempered cheese back into the pot. Add shredded cheese and stir until melted and smooth. Season with salt and pepper to taste.

In a small skillet, melt 2 tablespoons of butter and add breadcrumbs. Toast until golden, about 3–4 minutes, stirring. Remove from heat and mix in crumbled bacon.

Serve the soup hot in bowls, sprinkling the breadcrumb-bacon mixture on top for crunch.