Pound each chicken breast to an even 3/4-inch thickness using a meat mallet between two sheets of plastic wrap, then season both sides generously with salt and pepper. Set up three shallow bowls: flour in the first, beaten eggs mixed with Dijon mustard in the second, and crushed pretzels combined with garlic powder and smoked paprika in the third.

Dredge each chicken breast in flour, shaking off excess, then dip into the egg mixture, coating completely. Press the chicken firmly into the pretzel mixture, ensuring both sides are thoroughly coated. Place coated chicken on a wire rack and let rest for 10 minutes before cooking.

Preheat oven to 400°F. Place the coated chicken on a parchment-lined baking sheet. Brush the tops lightly with olive oil or melted butter and bake for 20 to 25 minutes, flipping halfway through, until golden brown and the internal temperature reaches 165°F.

While the chicken cooks, make the sauce by melting butter in a medium saucepan over medium heat. Whisk in flour and cook for 1 minute until it smells nutty but hasn't browned. Gradually pour in milk while whisking constantly to avoid lumps, then cook for 3 to 4 minutes until the mixture thickens to a heavy cream consistency.

Reduce heat to low and stir in both mustards until combined. Add the shredded cheddar cheese a handful at a time, stirring until each addition melts completely before adding more. If the sauce seizes up or gets grainy, add a tablespoon of milk and whisk vigorously. Season with salt and pepper to taste.

Serve the chicken immediately while hot and crispy, drizzled generously with the cheddar mustard sauce. Garnish with chopped fresh parsley and extra crushed pretzels if desired.