Season the pork cutlets with salt and pepper (I like 1 teaspoon salt and 1/2 teaspoon pepper). Dredge one cutlet in flour and shake to remove excess, then repeat with remaining cutlets.
In a large skillet over medium-high heat, heat oil until shimmering. Add pork cutlets in a single layer (working in batches if necessary) and cook until a golden brown crust forms on one side, about 4 to 5 minutes.
Flip the cutlets and continue cooking until the other side is browned and the chops are cooked through, reaching 145 degrees on an internal thermometer (8-10 minutes total). Transfer to a plate or rimmed baking sheet and repeat with any remaining cutlets, tenting the plate with foil to keep warm.
Add apples to the skillet and sauté until softened, about 4 to 5 minutes. Add apple juice and cook until the juice has mostly evaporated, about 3 to 4 minutes.
Stir in the cream and nutmeg. Simmer until thickened, about 2 to 3 minutes (you should be able to draw a line with your spoon through the sauce, and the line doesn't fill in). Season to taste with salt and pepper (I like 1/2 teaspoon salt and 1/4 teaspoon pepper).
Add pork cutlets back to the skillet and stir until heated through and coated with the sauce. Garnish with chives.