In a large pot, melt butter over medium heat. Add diced onion, carrots, and celery. Cook until vegetables are softened.
Add minced garlic and cook for an additional minute.
Stir in flour to create a roux, cooking for 2-3 minutes.
Gradually whisk in broth and beer, stirring constantly to avoid lumps.
Bring the soup to a simmer and let it thicken.
Reduce heat to low and add ¡Yo Quiero! Queso and shredded cheddar cheese. Stir until melted.
Season with salt and pepper to taste.
Ladle the soup into bowls, garnish with chives, and serve with optional garlic-rubbed toast.