Prepare chicken by butterflying the breasts into four thin pieces, approximately 1/4 inch thick.

Pulse salted pretzels in a food processor until fine crumbs, mix with paprika, salt, and pepper. Beat eggs with a splash of water in another dish.

Heat vegetable oil in a large non-stick skillet over medium-high heat until shimmering.

Dip each chicken piece in beaten eggs, then coat thoroughly in pretzel crumbs, pressing to adhere.

Fry chicken in the hot oil for 3-4 minutes on each side until golden brown, internal temperature reaches 165°F.

In a saucepan, melt butter and whisk in flour to create a roux. Gradually whisk in milk until thickened, about 3-5 minutes. Stir in cheese, mustard, paprika, and cayenne, seasoning to taste.

Serve chicken on a platter, drizzle with sauce, and garnish with parsley and red onion if desired.