Pat the skirt steak dry and trim any silver skin; set aside.
In a small bowl, combine the ground coffee, dark brown sugar, kosher salt, smoked paprika, black pepper, ground cumin, garlic powder, onion powder, and cayenne pepper.
Lightly coat the steak with the vegetable oil, then rub all over with the coffee spice mixture, pressing to adhere. Let stand 30–60 minutes at room temperature.
Preheat a grill or cast-iron skillet over high heat until very hot (grill about 500°F or skillet just smoking).
Sear the steak until deeply browned, 3–5 minutes per side, until an instant-read thermometer in the thickest part reads 125–130°F for medium-rare (cook longer to desired doneness).
Transfer to a cutting board and rest 5–10 minutes so juices redistribute.
Slice the steak thinly against the grain at a slight bias and serve with lime wedges for serving.