Preheat oven to 400°F (200°C) and line a baking sheet with a wire rack or parchment paper.
Set up a breading station with three shallow bowls: one with the 0.5 cup flour, garlic powder, and paprika; one with the eggs and yellow mustard whisked together; and one with the crushed pretzels.
Dredge each chicken breast in the flour mixture, dip into the egg wash, and then press firmly into the pretzel crumbs until fully coated.
Place the chicken on the prepared baking sheet and bake for 20 to 25 minutes until the internal temperature reaches 165°F (74°C).
While the chicken bakes, melt butter in a small saucepan over medium heat, then whisk in the sauce flour and cook for 60 seconds.
Slowly whisk in the milk and continue stirring until the mixture thickens and reaches a light simmer.
Reduce heat to low and stir in the shredded cheddar, Dijon mustard, and whole grain mustard until the cheese is completely melted and the sauce is smooth.
Season sauce with salt and pepper, then slice the chicken and drizzle with the warm mustard-cheddar sauce before serving.