In a large stockpot, melt the butter over medium heat. Add the carrots, peppers and 1/2 teaspoon salt and cook, stirring, until the vegetables are soft, about 5 minutes. Add the flour and cook, stirring, until well incorporated, about 5 minutes more.
Add the chicken stock, beer and half-and-half and cook, whisking often, at a very slow simmer over medium-low heat for 15 minutes.
Add the cheddar to the soup by the handful, whisking each batch until smooth. Add the Worcestershire, hot sauce, 1/2 teaspoon black pepper, the nutmeg, mustard and lemon juice, and stir to combine.
Puree the soup in batches in a blender (holding a thick towel over the lid to prevent overflow) until very smooth.
Just before serving, reheat the soup until steaming and taste for seasoning, adding salt as necessary. Ladle the soup into bowls and garnish each bowl with a swirl of mustard oil, a dollop of goat cheese and a sprinkle of thyme.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.
Adapted from "The New Midwestern Table" by Amy Thielen (c) Clarkson Potter, 2013. Provided courtesy of Amy Thielen. All rights reserved.