Preparation

• Position a rack in the center of the oven and heat the oven to 450°F.
   

Make the grits:

• In a 4-quart saucepan, bring the broth and milk to a boil over medium-high heat. Add the grits in a steady stream, whisking constantly. When they come to a boil, reduce the heat to low and cook, whisking occasionally, until the mixture begins to thicken, about 10 minutes. The grits will not be entirely tender at this point. Whisk in 1/2 cup warm water and continue to cook, whisking occasionally, until big, slow bubbles begin to pop on the surface, about 15 minutes more.
• Stir in the Cheddar, butter, Parmigiano, and hot sauce. Season to taste with plenty of salt and pepper and continue to cook, stirring often, until the flavors are well blended and the grits are creamy and tender, about 5 minutes more. Remove from the heat, cover, and keep warm on the back of the stove.

Roast the pork chops and fennel:

• Season the pork chops on both sides with the ground fennel and a generous amount of salt and pepper, pressing the seasonings into the chops to help them adhere.
• Heat the oil and 2 Tbs. of the butter in a 12-inch ovenproof skillet over medium-high heat. Add the herb sprigs and toss to coat with the fat. Arrange the chops in the skillet and cook undisturbed until deep golden-brown on the bottom, about 4 minutes. Flip the chops and cook until the other side is deep golden-brown, about 4 minutes more. Transfer the chops to a cutting board (they will not be fully cooked).
• Melt 2 Tbs. of the butter in the skillet over medium heat. Add the fennel and toss well to coat. Return the chops to the skillet and nestle them and the peaches into the fennel. Transfer the skillet to the oven and roast until an instant-read thermometer inserted into the thickest part of a chop reads 145°F, about 6 minutes.
• Top each chop with 1/2 Tbs. of the remaining butter and let the chops rest on a plate for at least 5 minutes. Serve with the grits, fennel, peaches, a drizzle of pan juices, and a fine grind of black pepper.