1/2 cup paprika
3 tablespoons ground black pepper
3 tablespoons coarse salt
3 tablespoons sugar
2 tablespoons chili powder
1 7 1/2- to 8-pound untrimmed whole beef brisket
12 ounces beer
1/2 cup cider vinegar
1/2 cup water
1/4 cup vegetable oil
2 tablespoons Worcestershire sauce
2 tablespoons minced jalapeño chilies
5 pounds (about) 100% natural lump charcoal
4 cups (about) oak or hickory wood smoke chips, soaked in cold water at least 30 minutes
1 cup purchased barbecue sauce (such as Bull’s-Eye)
1 tablespoon chili powder
Make dry rub:
Mix first 5 ingredients in small bowl to blend.
Transfer 1 tablespoon dry rub to another small bowl and reserve for mop. Spread remaining dry rub all over brisket. Cover with plastic; chill overnight.
Mix first 6 ingredients plus reserved dry rub in heavy medium saucepan. Stir over low heat 5 minutes. Pour 1/2 cup mop into bowl; cover and chill for use in sauce. Cover and chill remaining mop.
Following manufacturer’s instructions and using natural lump charcoal, start fire in smoker. When charcoal is ash gray, drain 1/2 cup wood chips and scatter over charcoal. Bring smoker to 200°F. to 225°F., regulating temperature by opening vents wider to increase temperature and closing slightly to reduce temperature.
Place brisket, fat side up, on rack in smoker. Cover; cook until tender when pierced with fork and meat thermometer inserted into center registers 185°F., about 10 hours (turn brisket over for last 30 minutes). Every 1 1/2 to 2 hours, add enough charcoal to maintain single layer and to maintain 200°F. to 225°F. temperature; add 1/2 cup drained wood chips. Brush brisket with chilled mop in pan each time smoker is opened. Transfer brisket to platter; let stand 15 minutes. (Can be made 1 day ahead. Cool 1 hour. Wrap in foil; chill. Before continuing, rewarm brisket, still wrapped, in 350°F. oven about 45 minutes.) Combine barbecue sauce and chili powder in heavy small saucepan. Add any accumulated juices from brisket and bring to boil, thinning sauce with some of reserved 1/2 cup mop, if desired.
Thinly slice brisket across grain. Serve, passing sauce separately