We "dry-brined" the pork before grilling it. This method calls for rubbing a mixture on the pork and chilling it. This allows for salt to pull seasonings into the meat and improve juiciness and flavor. It's unusual, but you do chill uncovered to keep the rub "dry." (Otherwise, the rub dilutes in trapped moisture.)
Stir together first 5 ingredients and 2 tsp. thyme. Trim pork roast. Rub paprika mixture over pork. Tie roast with kitchen string at 1 1/2-inch intervals, and place in a 13- x 9-inch baking dish. Chill, uncovered, 24 hours.
Light one side of grill, heating to 350° to 400° (medium-high) heat; leave other side unlit. Place pork over lit side, and grill, covered with lid, 8 minutes on each side or until browned. Transfer pork to unlit side, and grill, covered with lid, 35 to 45 minutes or until a meat thermometer inserted in thickest portion registers 145°. Let stand 10 minutes. Brush with Sticky Stout Barbecue Sauce. Sprinkle with remaining 2 tsp. thyme. Serve with remaining sauce.
Pair with: Charles Smith Wines Kungfu Girl Riesling (white) or Edmeades Mendocino County Zinfandel (red) or O'Dempsey's Big Red Ale beer (brewed in Atlanta, GA).
Mix together the paprika pork rub a couple hours ahead.