Heat a Dutch oven or large soup pot on the stove at medium heat and add the diced bacon.
6 slices bacon
Cook the bacon until crisp. Drain any excess bacon fat drippings.
Add the onions, carrots, celery, and garlic. Cook for 3-4 minutes or until the onions are translucent and fragrant.
½ cup diced onions, ½ cup diced carrots, ½ cup diced celery, 3-4 garlic cloves
Add in a small amount of the broth to deglaze the pot with your spoon. Use your spoon to scoop up any brown bits on the bottom of the pot. Leave these in the pot, it will have flavor from the bacon.
Sprinkle the flour throughout and stir to combine. Add it in stages to prevent clumping.
¼ cup flour
Pour in the remaining broth, beer, smoked paprika, cayenne pepper (Optional) salt, and pepper to taste. Stir.
12 oz beer, 2 cups broth, ½ teaspoon smoked paprika, salt and pepper to taste, ½ teaspoon cayenne pepper
Bring the mixture to a rolling boil and then lower the heat to simmer and cover the pot with the lid and lower the heat to low to let the soup simmer for about 15 minutes until the soup thickens.
Open the pot and add the heavy cream (or milk or half and half) and grated cheese. Stir until the soup thickens and the cheese melts. Taste repeatedly and make adjustments to the spices as necessary.
1 cup milk, half and half, or heavy cream, 3 cups grated cheddar cheese
Cool before serving.