How to Make It
Heat 1 Tbsp. unsalted butter in a large nonstick skillet over medium. Add yellow onion; cook, stirring occasionally, until lightly caramelized, about 15 minutes. Stir in minced garlic, fresh thyme leaves, and 1/4 tsp. each kosher salt and black pepper. Cook, stirring often, until fragrant, 1 to 2 minutes. Remove from heat; set aside.
Using a paring knife, cut a 2-inch slit in sides of bone-in, center-cut pork chops, creating a pocket, cutting to the bone. Stuff each with 1/4 cup shredded fontina cheese and 1 Tbsp. onion mixture. Set aside remaining onion mixture.
Preheat oven to 375°F. Heat 1 Tbsp. unsalted butter in nonstick skillet over medium-high. Sprinkle both sides of pork chops evenly with 1 tsp. each kosher salt and black pepper. Cook 2 stuffed pork chops in skillet, undisturbed, until golden brown on each side, about 3 minutes per side. Transfer pork chops to a wire rack set inside a rimmed baking sheet. Repeat with 1 Tbsp. unsalted butter and remaining pork chops.
Transfer baking sheet to preheated oven, and bake pork until a thermometer inserted in thickest portion registers 140°F, about 18 to 22 minutes. Remove from oven; let rest 10 minutes. While pork cooks, add russet potatoes to a large saucepan; cover with cold water. Bring to boil over medium-high, and simmer until tender, about 15 minutes. Drain and return potatoes to saucepan. Stir in whole milk, sour cream, 1 cup shredded fontina cheese, 4 Tbsp. unsalted butter, 1 1⁄2 tsp. kosher salt, and 1⁄4 tsp. black pepper until combined. Mash to desired consistency. Cover to keep warm.
Add chicken stock and remaining onion mixture to skillet over medium. Cook, stirring often, until slightly reduced, 5 to 6 minutes. Remove from heat, and stir in apple cider vinegar and 1 Tbsp. unsalted butter. Divide potatoes among 4 plates. Serve with pork chops, and top with sauce. Sprinkle with fresh thyme leaves.