1 cup unsalted butter
1 1/3 cups all-purpose flour
1 large yellow onion, diced
8 cloves garlic, minced
4 cups vegetable stock
1 cup whole milk
3 heads roasted garlic
1 tablespoon smoked paprika, plus more for serving
1/2 teaspoon ground cumin
2 1/4 pounds cheddar cheese, grated
chopped fresh chives, for garnish
Roast the garlic: Preheat oven to 350 degrees. Peel outermost of the papery skin from the garlic head. Using a knife cut the top 1/4 to 1/2 inch off of the top of the garlic, making sure to expose the individual cloves of garlic. Lightly cover with olive oil. Place on a baking sheet and bake until the garlic skin is light golden brown and cloves are tender when pressed, about 1 hour.
Melt 3/4 cup of the butter in a small saucepan over medium heat. Add the flour, whisking to avoid lumps. Cook, stirring frequently, until the flour takes on a light blond color, about 5 minutes. Remove from the heat and set aside.
Melt the remaining 1/4 cup butter in a large soup pot over medium heat. Stir in the onion and minced garlic and cook just until the garlic is aromatic, 30 seconds to 1 minute. Add the vegetable stock, beer, and milk. When the liquid begins to simmer, stir in the garlic, paprika, and cumin. Using a handheld immersion blender or a blender, puree until smooth. Whisk in the flour mixture until thoroughly combined. Add a handful of cheese at a time, whisking after each addition, until melted and smooth.
Season with salt and pepper to taste. Sprinkle with chives and paprika. Serve immediately.