Preheat oven to 375°F (190°C).
Pound chicken breasts to even thickness.
Season chicken with salt and pepper.
Set up three bowls: one with flour, one with eggs and milk (whisked), and one with crushed pretzels.
Coat each chicken breast in flour, then dip in egg mixture, and press into pretzels.
Heat oil in a skillet and brown chicken on both sides.
Transfer chicken to a baking sheet and bake for 15-20 minutes.
For the sauce, melt butter in a saucepan.
Whisk in flour and cook for 1 minute.
Gradually add milk, whisking until smooth.
Stir in cheese and mustard until melted and smooth.
Season sauce with salt and pepper.
Serve chicken with the warm sauce.