1 (2 3/4-pound) pork shoulder, butt portion
    (do not trim fat), cut into large chunks
4 teaspoons granulated sugar
1 tablespoon coarse kosher salt
2 tablespoons coarsely ground black pepper
3/4 teaspoon cayenne pepper
3/4 teaspoon crushed red pepper flakes
3/4 teaspoon dried thyme
1 tablespoon hot paprika
3/4 cup hickory chips

Put pork through a meat grinder, using disc with the largest holes. Add sugar, salt, peppers, thyme and paprika. Mix thoroughly. Cover and refrigerate for at least 1 hour. 

Lay a 20 x 10-inch single thickness of cheesecloth on a countertop. Paint a 4-inch wide strip along the long side of the cheesecloth with vegetable oil. Arrange 1 cup of the pork into a long thin strip along the inner border of the oil. Fold oiled cheesecloth over the pork and roll the strip back and forth to form an even sausage about 12 inches long. Roll the sausage up in the cheesecloth and tie each end in a knot or secure with string. Repeat with four more pieces of cheesecloth and remaining meat until you have 5 sausages.

Soak hickory chips in water for 30 minutes. 

Put a rectangular metal pan in the center of the bottom rack of a kettle grill and mound 15 charcoal briquettes on each side. Open the bottom vents on the grill. Light the charcoal and allow the fire to burn until the briquettes are ashen and glowing.

Drain hickory chips and distribute them over the charcoal. Place sausages on the grilling rack so that they are over the pan. Cover the grill, open the cover vents, and smoke the sausages for about 1 hour and 10 minutes, until they reach an internal temperature of 160 degrees F. Move the sausages to the edges of the grill, directly over the charcoal. Cook for 3 minutes, flip the sausages over, and cook for 3 minutes more on the other side. Remove the sausages from the grill. When they have cooled enough to handle, peel off the cheesecloth.

When cooked, this sausage can be kept in the refrigerator for 5 days and in the freezer for up to 6 months.