Broiled Chicken with Tomato Relish and Spaghetti

Name: Broiled Chicken with Tomato Relish and Spaghetti
Ingredients: 2 small whole broiler chickens, (about 2 to 2 1/2 pounds each); 4 sprigs thyme; 9 cloves garlic, crushed; 1 lemon juiced; 1/3 cup extra-virgin olive oil; Kosher salt; Freshly ground black pepper; 1 tablespoon paprika; 1 pint grape tomatoes; 1 bunch scallions, trimmed; 10 whole garlic cloves, unpeeled; 5 to 10 leaves basil, chopped; Extra-virgin olive oil, for drizzling; 1 tablespoon red wine vinegar; 1/4 teaspoon Worcestershire sauce; 1 pound spaghetti; 1/3 cup chopped flat-leaf parsley; 1/4 to 1/2 cup freshly grated Parmesan, optional