Step 1

Mix salt, paprika, brown sugar, pepper, and cinnamon in a small bowl. Pat turkey halves dry and cover all over with spice mix, packing on until you’ve used all of it. Arrange turkey halves, breast side up, on a rimmed baking sheet and chill, uncovered, at least 12 hours and up to 3 days.

Step 2

Let turkey sit at room temperature 1 hour before grilling. Pat dry with paper towels, then brush all over with 3 Tbsp. oil.

Step 3

Whisk chiles, vinegar, brown sugar, and ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt in a measuring glass or small bowl until sugar dissolves.

Step 4

Prepare a grill for medium indirect heat (for a charcoal grill, bank coals on one side of grill; for a gas grill, leave one or two burners off); lightly oil grate. Cover grill; heat to 350° (place an oven thermometer in the center of indirect side of grill if there isn’t one built in).

Step 5

Place turkey, skin side up, over indirect heat, with breast halves next to each other and farthest away from the heat (the legs should be closest to the heat). Cover grill and grill turkey, basting skin with chile sauce every 20 minutes, until an instant-read thermometer inserted into thickest part of breasts registers 140° and thickest part of legs registers 160°, 1¼–1¾ hours. Keep an eye on the temperature inside the grill and aim to maintain heat at 350° as much as possible. If using a gas grill and the temperature drops significantly, turn on a second burner to medium-low to bring the temperature back up. If using a charcoal grill, light a chimney of coals and add as needed.

Step 6

Lightly oil grate on hot side of grill. Using tongs and a large spatula to support the turkey, turn turkey halves over, arranging skin side down over direct heat. Brush turkey with chile sauce (you won’t use all of it) and grill, uncovered, until skin is charred and crisp, 8–10 minutes. Thickest part of breasts should now register 150° on thermometer and legs should register 170°. Arrange rosemary sprigs over a cutting board and set turkey, skin side up, on top. Let rest 30–60 minutes before carving.

Step 7

While the turkey rests, bring remaining chile sauce to a simmer in a small saucepan over medium heat. Whisk in butter a piece at a time, incorporating completely after each addition. Stir in Worcestershire sauce; season with salt.

Step 8

Carve turkey as desired and transfer to a platter; arrange rosemary around. Pour sauce over turkey, along with any accumulated juices on cutting board.