Brine the chicken: In a large bowl or container, combine the buttermilk and 2 tablespoons of salt. Add the chicken to the brine, making sure to submerge fully. Cover and refrigerate for at least 2 hours, or overnight. When ready to use, remove the chicken wings from the brine and pat dry with paper towels. Transfer to a wire rack set over a baking sheet.
Preheat the oven to 300°F (150°C).
Fill a large cast iron skillet ¾ of the way with peanut oil and heat over medium-high heat until the temperature reaches 350°F (180°C).
In a small bowl, whisk together 2 tablespoons salt, the onion powder, paprika, garlic powder, black pepper, poultry seasoning, cayenne, and ground mustard until well combined.
Transfer all but 2 tablespoons of the spice mixture to a medium bowl with the flour and cornstarch and whisk until well combined.
In a separate medium bowl, whisk together the eggs, buttermilk, hot sauce, and a pinch of salt until well combined.
Coat a chicken wing in the flour mixture, shaking off any excess, then dip in the buttermilk mixture, letting any excess drip off. Coat again in the flour mixture, pressing the flour into the chicken. Return the coated chicken to the wire rack and repeat with the remaining wings.
Working with 2–3 wings at a time, fry the chicken in the hot oil until golden brown and the internal temperature reaches 160-165°F (70-75°C). Remove the chicken from the oil, sprinkle on both sides with a pinch of the reserved spice mix, then set on a clean wire rack set over a baking sheet to cool. Repeat with the remaining chicken. When finished frying, transfer the chicken to the oven to keep warm until ready to serve.
Make the waffles: Melt the butter in a medium nonstick saucepan over medium-high heat. Cook, stirring occasionally, until the butter turns dark brown and smells nutty, between 7-10 minutes. Watch carefully and focus on color, so the butter does not burn, aiming from brown not black bits. Remove the pot from the heat.
Add an ice cube to the butter and slowly let it melt. It may froth and bubble. Add the remaining ice cube and gently stir until melted. Pour ½ cup of the browned butter into a liquid measuring cup or heatproof bowl and let cool completely, about 5 minutes. Store any remaining browned butter in the refrigerator for another use.
Preheat a waffle iron to medium-high heat.
In a large bowl, whisk together the flour, sugar, baking powder, baking soda, and salt.
In a medium bowl or large liquid measuring cup, whisk together the buttermilk, browned butter, eggs, and vanilla until well combined.
Pour the wet ingredients into the dry ingredients and whisk until just combined, being careful not to overmix. Let the batter sit for 5–7 minutes while the leavening agents activate.
Grease the waffle iron with nonstick spray, then cook the waffles according to the manufacturer’s instructions. You should have about 6 total, depending on the waffle iron. Set the waffles on a baking sheet as they finish cooking and transfer to the oven with the chicken to keep warm until ready to serve.
To serve, place a waffle on each plate (either whole or cut into 4 pieces) and set 2–3 wings on top of or next to each waffle. Top the waffles with butter, maple syrup, and/or hot sauce, if desired. Serve hot.
Any leftover waffles can be wrapped individually in plastic wrap, then placed in a zip-top bag and stored in the refrigerator for up to 2 days.