Preheat oven to 400°F (200°C) and line a baking sheet with parchment paper.
Season chicken breasts with salt, pepper, garlic powder, and onion powder on all sides, patting seasonings into the meat.
Place flour in first shallow bowl. Beat eggs with 1 tablespoon Dijon mustard in second bowl. Add crushed pretzels to third bowl.
Coat each chicken breast in flour, then egg mixture, then pretzel crumbs, pressing firmly into all sides including edges to adhere. Place on prepared baking sheet.
Bake for 25-30 minutes until internal temperature reaches 165°F (75°C) and crust is golden brown and crispy.
While chicken bakes, combine 1/2 cup milk, 2 tablespoons Dijon mustard, and Worcestershire sauce in small saucepan over medium heat. Stir until steaming (around 180°F) but not boiling.
Reduce heat to low and gradually add 1/2 cup shredded cheddar cheese, stirring continuously until smooth. Season with salt and pepper. Remove from heat.
Let baked chicken rest 3-4 minutes, then drizzle with warm mustard-cheddar sauce and serve immediately.
Notes
Use thick-cut hard pretzels for best texture. Crush coarsely using a rolling pin in a sealed plastic bag.
Shred cheese from a block rather than using pre-shredded for smoothest sauce.
Pound chicken breasts to even 1-inch thickness before breading for uniform cooking.
Pat chicken dry before breading for better coating adhesion.
Store leftovers separately (chicken and sauce) for up to 3 days. Reheat chicken in 350°F oven on wire rack to maintain crispiness.
Freeze uncooked breaded chicken for up to 2 months. Bake from frozen, adding 10-15 minutes to cooking time.