For the liquid gold honey mustard sauce: Combine the mustard, vinegar, honey, Worcestershire sauce, vanilla, hot sauce and pepper in a small saucepan and cook over medium heat, whisking constantly, until boiling, about 5 minutes. Reduce the heat to low and lightly simmer until the sugar dissolves, about 5 minutes.
For the chicken: If you're baking the chicken, preheat the oven to 450 degrees F and fit a wire rack inside a large rimmed baking sheet and coat with nonstick cooking spray. If using a deep-fryer, preheat the oil to 350 degrees F.
Place the chicken in a resealable plastic bag with 1/2 cup of the Liquid Gold Honey Mustard Sauce. The chicken can be dredged immediately, or it can be marinated for at least 2 hours or up to 8 hours, if time allows.
Put the pretzels in a food processor and pulse until finely chopped, about 10 pulses.
Prepare your dredging station. Place the flour in a shallow bowl. Next to that, a second shallow bowl with the eggs, and next to that, a third shallow bowl with the pulverized pretzels.
Remove the chicken pieces from the mustard sauce, season them with salt and pepper, lightly dust them with the flour, then dip them in the eggs, then dip them in the pulverized pretzels until they are entirely coated.
If baking, place the chicken on the prepared wire rack and bake until the internal temperature registers 165 degrees F on an instant-read thermometer, 12 to 14 minutes.
If using a deep-fryer, place the chicken gently into the oil and fry in two or three batches until golden and the internal temperature registers 165 degrees F on an instant-read thermometer, 4 to 5 minutes. Remove with a spider and drain on a paper towel-lined plate.
For the beer cheese sauce: Heat a medium saucepan over low heat. Add the evaporated milk, lager, mustard and Worcestershire sauce and whisk together until uniform and smooth. Toss the grated cheeses and cornstarch together in a bowl until the cheese is completely coated. Whisk the cheese into the milk mixture and cook, whisking constantly, until the cheese melts completely and the sauce is silky and smooth, about 5 minutes.
To serve, top the chicken with the chopped parsley and serve with the remaining Liquid Gold Honey Mustard Sauce and the Beer Cheese Sauce for dipping.