Feta Roast Chicken
1 (4 ounce) package feta cheese 1 (5 pound) whole chicken 1 lemon, zested and juiced 1 pinch cayenne pepper 1 teaspoon freshly ground black pepper 2 sprigs fresh oregano 2 sprigs fresh rosemary 2 tablespoons chicken broth, or as needed 2 teaspoons dried oregano 2 teaspoons olive oil 3 cloves garlic, crushed 3 tablespoons olive oil, or as needed kitchen string kosher salt to taste salt to taste ½ teaspoon red pepper flakes, or to taste