Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper.
In a shallow bowl, combine the crushed pretzels, garlic powder, onion powder, paprika, black pepper, and salt.
In another shallow bowl, place the flour. In a third bowl, beat the eggs.
Dip each chicken breast first into the flour, shaking off the excess, then into the beaten eggs, and finally into the pretzel mixture, pressing gently to adhere.
Place the coated chicken breasts on the prepared baking sheet and drizzle with olive oil. Bake for 25-30 minutes, or until the chicken is cooked through and the crust is golden brown.
While the chicken is baking, prepare the mustard cheddar sauce. In a small saucepan over medium heat, melt the butter. Stir in the flour and cook for 1 minute.
Gradually whisk in the milk, stirring constantly until the mixture thickens.
Remove from heat and stir in the shredded cheddar cheese, Dijon mustard, garlic powder, and season with salt and pepper to taste.
Once the chicken is done, remove it from the oven and let it rest for a few minutes before slicing. Serve with the mustard cheddar sauce drizzled on top.