Szechuan Noodles with Chicken and Broccoli

Name: Szechuan Noodles with Chicken and Broccoli
Ingredients: 3 whole (6 split) chicken breasts, bone-in, skin-on; Good olive oil; Kosher salt and freshly ground black pepper; 1 bunch broccoli, cut into florets and stems discarded; 6 garlic cloves, chopped; 1/4 cup fresh ginger, peeled and chopped; 1/2 cup vegetable oil; 1/2 cup tahini (sesame paste); 1/2 cup smooth peanut butter; 1/2 cup good soy sauce; 1/4 cup dry sherry; 1/4 cup sherry vinegar; 1/4 cup honey; 1/2 teaspoon Asian hot chili oil; 2 tablespoons dark toasted sesame oil; 1/8 teaspoon ground cayenne pepper; 1 pound spaghetti; 4 scallions, sliced diagonally (white and green parts); 1 yellow bell pepper, julienned; 1 red bell pepper, julienned