Use a stainless-steel pan for pork to get superhigh heat, which makes for better browning.
Warm a large skillet over medium-high heat; season pork on both sides with salt and pepper. Add 2 tsp. oil to skillet; swirl to coat. Add pork and cook until deeply golden, about 3 minutes. Turn and cook until just cooked through, 2 to 3 minutes longer. Transfer to a platter and tent with foil to keep warm.
Add remaining 1 tsp. oil, shallot and sage to skillet; sauté for 30 seconds to 1 minute. Add vinegar and cider and cook, stirring to release brown bits from bottom of skillet, until liquid has reduced by about half, about 1 minute. Remove skillet from heat; add mustard and butter and swirl until sauce is creamy. Spoon sauce over pork and serve immediately.