Step 1
Whisk ⅓ cup double-concentrated tomato paste, 1 Tbsp. garlic powder, 1 Tbsp. Italian seasoning, 1 Tbsp. smoked paprika, ¼ cup white wine vinegar, ¼ cup extra-virgin olive oil, and 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt in a medium bowl. Add 2 lb. chicken wings, flats and drumettes separated, patted dry, and toss to coat. Cover and chill at least 1 hour and, preferably, up to 3 hours.
Step 2
Meanwhile, place ½ medium head of cauliflower, cut into florets, 1 large carrot, peeled, cut into 3″-long sticks, 3 celery stalks, cut into 3″-long sticks, and ½ cup pickled hot cherry peppers, halved, in a medium heatproof bowl. Bring 2 Tbsp. sugar and remaining 1 cup white wine vinegar and 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt to a simmer in a small saucepan, stirring to dissolve sugar. Remove from heat and stir in ¼ cup cherry pepper brine; pour mixture over vegetables. Let sit 15 minutes, then chill until ready to serve.
Step 3
Combine 12 oz. feta and 2 Tbsp. buttermilk or sour cream in a food processor; season generously with freshly ground pepper. Process until very smooth, about 3 minutes. Set whipped feta aside.
Step 4
Prepare a grill for medium heat; oil grate. Remove chicken wings from marinade, letting excess drip back into bowl, and arrange on grate. Cover and grill, turning occasionally, until charred in spots and an instant-read thermometer inserted into thickest part of a wing registers 165°, 20–25 minutes.
Step 5
To serve, spread reserved whipped feta on a platter; arrange chicken wings on top. Tuck drained pickled vegetables around. Drizzle hot honey over.
Do Ahead: Vegetables can be pickled 1 day ahead. Cover and keep chilled.