Pat the chicken legs dry and season them with 4 teaspoons of kosher salt and 2 teaspoons of black pepper.
Heat 1 tablespoon extra virgin olive oil in a wide, ovenproof pot over medium-high heat. Once hot, add the chicken, skin-side down, and cook without moving for 5 minutes. Flip and cook for 3 minutes. Transfer to a plate.
Sauté the onion and fennel:
Add the sliced onion and fennel to the pot and sauté for 5 to 7 minutes until softened. Season lightly with salt and pepper. Add the minced garlic and chopped Calabrian chili peppers. Sauté for 30 seconds until fragrant.
Add the chicken stock and bring to a boil. Turn off the heat.
Arrange the chicken, skin-side up, in the pot. Transfer the chicken to the oven and roast for 35 to 45 minutes, or until the internal temperature reaches 165°F at the thickest part of the leg.
Cook the pasta:
As the chicken roasts, bring a large pot of salted water to a boil. Add the pasta and cook according to package directions. Reserve ¼ cup of the pasta water and drain the pasta. Set aside.
Broil the chicken (optional):
Turn on the broiler and broil for 2 to 3 minutes to brown the skin further. Remove from the oven.
Finish the sauce:
Carefully transfer the chicken to a large serving platter. Spoon 3 to 4 tablespoons of sauce from the pot over the chicken. Tent the chicken with foil as you finish the sauce.
Bring the sauce in the pot to a boil. Tear the basil and add it to the sauce along with the grated Parmigiano-Reggiano. Whisk to incorporate. Reduce the heat to medium-low and rapid-simmer for 5 minutes until the sauce reduces and thickens. Taste and season.
Add the cooked pasta to the sauce along with a few splashes of the reserved pasta water. Stir to coat. Simmer for 1 to 2 minutes. Turn off the heat.
Transfer the pasta to a serving platter. Finish with a few basil leaves and more grated Parmigiano-Reggiano, if desired.
To serve:
Spoon the pasta onto plates and serve with a chicken leg. Enjoy!