Heat the oven to 350 degrees . Cut the bread into 3-inch rounds or trim into slider-size squares. Arrange on a baking sheet and bake until lightly toasted and golden, 8 to 10 minutes.
Combine the meat with the garlic, onion, paprika, beer, salt and pepper. Mix and form 8 burgers (about 3 ounces each) and drizzle with oil. Heat a griddle pan or large cast-iron skillet over medium-high heat. Cook the patties for 3 to 4 minutes on each side.
Meanwhile, in a saucepan, melt the butter over medium heat. Whisk in the flour and milk and simmer to thicken for about 3 minutes; season with salt and pepper. Melt in the cheese and stir in the pimientos, mustard and hot sauce.
Divide the patties among 8 toast slices and top with the cheese sauce and another slice of toast. Garnish with the pickles and secure with toothpicks.