Preheat oven to 400°. Set a wire baking rack on a rimmed foil-lined baking sheet and spray the rack with olive oil.
Pulse pretzels in a food processor until mostly ground, with pieces no larger than 1/4-inch.
Pour flour into one dish; eggs, mustard, salt, & pepper into another dish; and crushed pretzels into a third dish. Whisk eggs until smooth.
Lay chicken thighs flat and pound to 1/4-inch thick.
Dredge chicken in flour, coat in egg, and press both sides into pretzels until thoroughly coated. Set chicken on the wire baking rack and lightly spray the tops with olive oil.
Bake at 400° for 8 minutes, then flip chicken over. Spray the tops with olive oil and return to the oven for 6-8 minutes, until golden brown.
While the chicken is baking, make the beer cheese sauce, below.
Drizzle chicken generously with hot beer cheese and serve right away.