FOR THE SHALLOT BUTTER (OPTIONAL):
Heat an air fryer to 375ºF. Meanwhile, trim 1 pound Brussels sprouts and halve any that are larger than 1-inch wide. Transfer to a medium bowl, add 1 tablespoon olive oil and 1/2 teaspoon kosher salt, and toss to combine.
Add the Brussels sprouts to the air fryer and arrange into a single layer (air fry in batches if needed). Air fry, stopping to shake the basket (or rotate the pans in larger air fryers) about halfway through, until browned and tender, about 15 minutes total. Meanwhile, make the shallot butter if desired.
Finely chop 1 medium shallot. Place 2 tablespoons unsalted butter in a medium microwave-safe bowl and melt in the microwave. (Alternatively, melt in a medium saucepan over low heat, then remove from the heat.) Add the shallots and 1 teaspoon red wine vinegar, and stir to combine.
When the Brussels sprouts are ready, transfer into the bowl or saucepan with the shallot butter and toss to combine. Serve immediately.