Season both sides of pork cheeks with salt and pepper. Sprinkle with flour and press it into the meat to coat thoroughly.

Heat clarified butter in a pan over medium-high heat. Sear meat on both sides until richly browned, adjusting heat lower if necessary. When cheeks are browned, reduce heat to medium. Transfer cheeks to a plate to rest.

Remove all but 2 tablespoons fat from the skillet. Add onions, carrots, and celery to skillet. Cook and stir until softened and sweet, seasoning with a pinch of salt. Add vinegar and stir to deglaze the pan. Pour in the cider and chicken stock. Bring to a simmer. Add sage and rosemary. Reduce heat to low and transfer cheeks back to pan. Cover. Cook until fork tender but not falling apart, 2 to 3 hours depending on the size of the pork cheeks. Transfer to a plate.

Bring liquid to a boil over high heat, skimming off fat as it rises to the surface. Reduce volume of liquid by about 60 to 70%. Sauce will start to thicken up. Taste for salt and season as needed. Transfer cheeks back to liquid. Continue to cook over medium-low heat until cheeks are heated through and tender and sauce is thick enough to coat cheeks.