Chef John's Chicken Spaghetti

Ingredients (10)

• + 1 (4.5 pound) whole chicken, giblets removed add to pantry
• + 1 (24 ounce) jar marinara sauce add to pantry
• + 6 cups water add to pantry
• + 2 anchovy fillets add to pantry
• + ½ teaspoon red pepper flakes, or to taste add to pantry
• + 2 teaspoons salt, plus more to taste add to pantry
• ✓ 1 (16 ounce) package spaghetti
• + ¼ cup thinly sliced basil leaves add to pantry
• + ½ cup grated Pecorino Romano cheese add to pantry
• + 1 tablespoon cold butter add to pantry