Remove the silverskin from each pork tenderloin. Slide a paring knife under the shiny membrane, grip the loosened end with a paper towel, and peel it off in strips. Trim the thin tail end if needed for even cooking.
Mix all dry rub ingredients together in a small bowl: brown sugar, smoked paprika, garlic powder, onion powder, kosher salt, black pepper, and cayenne.
Optional: Apply a thin coat of yellow mustard all over each tenderloin as a binder. Apply the dry rub generously on all sides and press it in firmly with your hands.
Preheat your smoker to 225°F. Add apple wood (or cherry or pecan) and allow the smoker to reach a stable temperature with clean smoke — about 15 minutes.
Place the tenderloins directly on the grill grates with at least 1 inch of space between them. Insert a probe thermometer into the thickest part of one tenderloin.
Smoke at 225°F until the internal temperature reaches 140°F — approximately 1.5 to 2 hours. Optional: spritz with apple juice every 30 minutes. Avoid opening the smoker unnecessarily.
Optional BBQ glaze: when the internal temperature reaches 135°F, brush a thin layer of BBQ sauce on all sides. Close the lid and let it tighten as the temperature climbs to 140°F.
Remove the tenderloins from the smoker at 140°F internal temperature. Tent loosely with aluminum foil and rest for 10 to 15 minutes. Carryover cooking will bring the internal temperature to 145°F.
Slice the rested tenderloins into ½-inch-thick medallions, cutting against the grain. Serve immediately.