Preheat the oven to 400°F. Line a baking sheet with parchment paper.
In a shallow dish, combine crushed pretzels, garlic powder, onion powder, paprika, salt, and pepper. In another shallow dish, place the flour. In a third dish, beat the eggs.
Pat the chicken breasts dry with paper towels. Dredge each breast in flour, shaking off excess, then dip into the beaten eggs, and finally coat with the pretzel mixture, pressing firmly to adhere.
Heat olive oil in a large skillet over medium heat. Add the chicken breasts and cook for about 3-4 minutes on each side until golden brown. Transfer the chicken to the prepared baking sheet and bake for 15-20 minutes or until the internal temperature reaches 165°F.
While the chicken is baking, prepare the mustard cheddar sauce. In a saucepan, melt the butter over medium heat. Whisk in the flour and cook for 1 minute. Gradually whisk in the milk and cook until thickened, about 3-5 minutes. Stir in the cheddar cheese and Dijon mustard until smooth. Season with salt and pepper to taste.
Serve the pretzel-crusted chicken drizzled with mustard cheddar sauce.