Lemon Broiled Chicken with Bulgur Salad

Name: Lemon Broiled Chicken with Bulgur Salad
Ingredients: 1 cup bulgur wheat; Kosher salt and freshly ground black pepper; 1/2 cup lemon juice (from 4 to 6 lemons); 1 tablespoon Dijon mustard; 4 cloves garlic, minced; 1 small shallot, minced; 1 cup extra-virgin olive oil; 8 boneless, skin-on chicken pieces (4 breasts and 4 thighs), trimmed of excess fat; 1 cup halved grape tomatoes; 1/2 cup chopped fresh parsley; 1/4 cup packed chopped fresh mint; 2/3 English cucumber, diced (about 1 cup)