Whisk together the mayonnaise, mustard, lemon zest and juice, garlic and 1/2 teaspoon salt. Refrigerate until ready to serve.
For the wings:
Preheat the oven to 425 degrees F. Generously coat 2 rimmed baking sheets with oil.
Toss the wings with 2 teaspoons salt and a few grinds of pepper in a large bowl and divide them between the prepared baking sheets, spreading them in a single layer. Bake until very crispy, about 55 minutes.
Meanwhile, combine the beer, barbecue sauce, brown sugar and hot sauce in a small saucepan and bring to a boil over medium-high heat. Reduce the heat slightly and simmer briskly until the liquid becomes syrupy and is thick enough to coat the back of a spoon, about 20 minutes.
Transfer the baked wings to a clean large bowl and toss them with the beer-barbecue glaze. Serve with the dipping sauce.
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