Preheat oven to 375 degrees. Place parchment paper in the bottom of a rimmed baking sheet. Place a rack on top of the paper and spray with cooking spray. Set aside.
Place the flour, onion, garlic, and black pepper in a shallow dish and mix to combine. Set aside.
The second shallow dish will have the egg and the Dijon mustard. Whisk together. Set aside.
Take the pretzels and crush them inside a quart-sized resealable plastic bag with a rolling pin. You want some texture, so don’t crush them to dust—place in the third shallow dish.
Dip each chicken breast in the flour mixture and shake off any excess.
Then dip the chicken into the egg mixture, making sure it is fully coated. Let the excess drop off, but don’t shake it off.
Place the chicken piece in the crushed pretzels. Press gently to help the pretzels adhere.
Place the completed breaded chicken pieces on the rack in the baking sheet. Bake for 20-25 minutes or until the chicken reaches 165℉ at the thickest part.
During the last 5 minutes of baking time, prepare the cheese sauce. In a small saucepan, melt the butter over low heat. Add the nutmeg and dry mustard. Whisk in the milk and heat for 30 seconds. Whisk in the cheese, stirring constantly. Cheese sauce should be smooth.
Serve the chicken immediately, topped with 1 1/2 Tbsp of the cheese sauce.