1. 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.
2. 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.