Preparation Prepare a grill for 2-zone heat (for a charcoal grill, bank two-thirds of coals over one side of grill and scatter remaining coals over the other side; for a gas grill, set one burner to medium-high heat and the remaining burners to medium-low heat). Clean and lightly oil grate. Mix vinegar, brown sugar, honey, Worcestershire, garlic powder, paprika, cayenne, and 1/2 cup mustard in a medium bowl; set aside. Season chicken on all sides with 2 Tbsp. plus 2 tsp. salt. Grill chicken skin side down over direct heat, turning halfway through or whenever there is a flare, until lightly charred, 5-8 minutes. Move chicken to cooler part of grill, cover with lid, and continue to grill, turning several times and keeping covered, until an instant-read thermometer inserted into the thickest part of the breast registers 140°F, 15–20 minutes. The smaller pieces will go more quickly ,and you can transfer them to a rimmed baking sheet until all pieces are ready. Uncover grill and return any pieces from baking sheet back to grill. Using a brush, generously baste chicken with reserved sauce. Continue to grill, turning every 1–2 minutes and basting the other side, until the internal temperature of thickest part of breast registers 155°F and sauce is shiny and lacquered, about 6 minutes. Transfer chicken to a cutting board as pieces are done (again, the smaller pieces will go more quickly). Let rest 10 minutes before separating drumsticks from thighs and slicing chicken breast in half on a bias. While chicken rests, gently toss onions, 2 Tbsp. oil, and 1 tsp. salt in a medium bowl, being careful not to break up onion rounds into rings. Grill over medium-low heat, turning once, until charred on both sides and tender, 10–15 minutes. Whisk 2 Tbsp. bean pickling liquid and remaining 2 Tbsp. mustard in a large bowl. Drain beans and add to bowl. Add tomatoes and grilled onions. Toss to combine; season with salt. Arrange chicken on a large platter and serve with salad alongside. Do Ahead: Sauce can be made 3 days ahead. Cover and chill.
Preparation Prepare a grill for 2-zone heat (for a charcoal grill, bank two-thirds of coals over one side of grill and scatter remaining coals over the other side; for a gas grill, set one burner to medium-high heat and the remaining burners to medium-low heat). Clean and lightly oil grate. Mix vinegar, brown sugar, honey, Worcestershire, garlic powder, paprika, cayenne, and 1/2 cup mustard in a medium bowl; set aside. Season chicken on all sides with 2 Tbsp. plus 2 tsp. salt. Grill chicken skin side down over direct heat, turning halfway through or whenever there is a flare, until lightly charred, 5-8 minutes. Move chicken to cooler part of grill, cover with lid, and continue to grill, turning several times and keeping covered, until an instant-read thermometer inserted into the thickest part of the breast registers 140°F, 15–20 minutes. The smaller pieces will go more quickly ,and you can transfer them to a rimmed baking sheet until all pieces are ready. Uncover grill and return any pieces from baking sheet back to grill. Using a brush, generously baste chicken with reserved sauce. Continue to grill, turning every 1–2 minutes and basting the other side, until the internal temperature of thickest part of breast registers 155°F and sauce is shiny and lacquered, about 6 minutes. Transfer chicken to a cutting board as pieces are done (again, the smaller pieces will go more quickly). Let rest 10 minutes before separating drumsticks from thighs and slicing chicken breast in half on a bias. While chicken rests, gently toss onions, 2 Tbsp. oil, and 1 tsp. salt in a medium bowl, being careful not to break up onion rounds into rings. Grill over medium-low heat, turning once, until charred on both sides and tender, 10–15 minutes. Whisk 2 Tbsp. bean pickling liquid and remaining 2 Tbsp. mustard in a large bowl. Drain beans and add to bowl. Add tomatoes and grilled onions. Toss to combine; season with salt. Arrange chicken on a large platter and serve with salad alongside. Do Ahead: Sauce can be made 3 days ahead. Cover and chill.