2 Tbsp. extra-virgin olive oil, plus more for grill
1/4 cup apple cider vinegar
1/4 cup (packed) light brown sugar
2 Tbsp. honey
2 tsp. Worcestershire sauce
1 tsp. garlic powder
1 tsp. paprika
1/4 tsp. cayenne pepper
1/2 cup plus 2 Tbsp. country-style mustard
5–6 lb. skin-on, bone-in chicken breasts and/or whole legs
2 Tbsp. plus 3 tsp. kosher salt, divided, plus more
2 large sweet onions, sliced into 1/2"-thick rounds
1 (15-oz.) jar pickled green beans
2 lb. tomatoes, halved if large, sliced into 1/2"-thick rounds