Simmer 2 cups broth and potato in a small saucepan. Cook 15 minutes or until potato is tender. Transfer potato mixture to a blender. Remove center piece of blender lid (to allow steam to escape); secure blender lid on blender. Place a clean towel over opening in blender lid (to avoid spills). Blend until smooth. Set mixture aside.
Heat a large Dutch oven over medium heat. Coat pan with cooking spray. Add onion, celery, and carrot to pan; cook 5 minutes or until tender, stirring occasionally. Add garlic to pan; cook 30 seconds.
Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, remaining 2 1/2 cups broth, and milk in a medium bowl; stir with a whisk. Add flour mixture to pan; bring to a boil. Cook 1 minute or until slightly thick; stir constantly with a whisk. Add potato mixture, sharp cheddar cheese, and next 5 ingredients (through salt) to pan; cook for 1 minute or until cheese melts, stirring constantly. Add beer to pan; bring to a simmer. Cook 15 minutes or until thoroughly heated. Garnish with black pepper, if desired.