Preheat your 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, salt, and pepper.
In another shallow bowl, place the flour. In a third bowl, beat the eggs.
Pat the chicken breasts dry with paper towels. Dredge each breast in flour, shaking off the excess, then dip into the beaten eggs, and finally coat with the pretzel mixture, pressing gently to adhere.
Heat the olive oil in a large oven-safe skillet over medium heat. Once hot, add the coated chicken breasts and cook for about 3-4 minutes per side, until golden brown.
Transfer the skillet to the preheated oven and bake for 15-20 minutes, or until the chicken is cooked through (internal temperature should reach 165°F).
While the chicken is baking, prepare the mustard-cheddar sauce. In a small saucepan over medium heat, combine the heavy cream, Dijon mustard, and honey. Stir until heated through. Gradually add the shredded cheddar cheese, stirring until melted and smooth. 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. Serve the chicken drizzled with the mustard-cheddar sauce.