In a large Dutch oven, melt 3 tablespoons butter over medium heat. Add onion, carrot, apple, salt, and black pepper; cook until mixture becomes tender, about 5 minutes. Add dry mustard, red pepper, and garlic; cook, stirring often, until mixture is very tender, about 3 minutes. Add flour; cook, stirring constantly, for 3 minutes.
Reduce heat to medium-low, and slowly add beer, stock, and milk, stirring constantly. Increase heat to medium-high, and boil, stirring constantly, until thickened, about 3 minutes. Remove from heat; let stand for 3 minutes.
Working in batches, blend mixture in a blender until very smooth. Return mixture to Dutch oven and heat over medium-low. Working in batches, add cheeses, stirring until cheese melts.
In a small skillet, melt remaining 2 tablespoons butter over medium-high heat. Add bread, stirring constantly until toasted, about 5 minutes. Top each serving with croutons and pecans.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/apple-beer-cheese-soup/