Step 1: Prepare your dredging station. In a shallow dish, place the 1 cup of all-purpose flour. In a second shallow dish, whisk the 2 large eggs with 1 teaspoon garlic powder, 1 teaspoon onion powder, salt, and pepper.
Step 2: In a third shallow dish, place the 2 cups of coarsely crushed pretzels.
Step 3: Pat the chicken breasts dry with paper towels. Dredge each chicken breast first in the flour, shaking off any excess. Then dip it into the egg mixture, ensuring it's fully coated. Finally, press it firmly into the crushed pretzels, making sure all sides are well-covered.
Step 4: Heat 2 tablespoons of vegetable oil in a large skillet over medium heat.
Step 5: Carefully place the coated chicken breasts in the hot skillet. Cook for 6-8 minutes per side, or until the chicken is golden brown, cooked through, and reaches an internal temperature of 165°F (74°C). You may need to cook in batches depending on your skillet size. Remove from skillet and set aside.
Step 6: While the chicken cooks, prepare the Creamy Mustard-Cheddar Sauce. In a small saucepan, melt 1 tablespoon of unsalted butter over medium heat.
Step 7: Whisk in 1 tablespoon of all-purpose flour and cook for 1 minute, stirring constantly, to create a roux.
Step 8: Gradually whisk in ½ cup of milk, stirring until the mixture is smooth and begins to thicken. Bring to a gentle simmer.
Step 9: Remove from heat and stir in 1 tablespoon of Dijon mustard and ½ cup of shredded sharp cheddar cheese until the cheese is melted and the sauce is smooth and creamy. Season with a pinch of salt and pepper if desired.
Step 10: Serve the pretzel-crusted chicken immediately, drizzled generously with the warm Creamy Mustard-Cheddar Sauce.