Remove 4 fully thawed turkey drumsticks from their packaging and pat them thoroughly dry with paper towels. Check that the skin is intact and the drumsticks fit comfortably in the 6-quart (5.7 L) slow cooker. Removing excess surface moisture helps the olive oil and dry seasonings coat the meat evenly. Allow approximately 3 minutes for this preparation.

In a small mixing bowl, combine 1 teaspoon (6 g) fine salt, 1 teaspoon (2 g) smoked paprika, 1 teaspoon (3 g) garlic powder, 1 teaspoon (2.5 g) onion powder, 1 teaspoon (1 g) dried thyme, 1/2 teaspoon (0.5 g) crushed dried rosemary, and 1/2 teaspoon (1 g) freshly ground black pepper. Stir for approximately 1 minute, until the mixture has a uniform reddish-brown color and the herbs are evenly distributed.

Rub 1 tablespoon (15 ml) olive oil over all 4 turkey drumsticks. Sprinkle the prepared seasoning mixture evenly over the skin and exposed meat, rubbing gently to coat every side. Spend approximately 3 minutes distributing the seasonings. The surfaces should appear lightly glossy with a uniform coating of spices, rather than showing dry patches.

Pour 1 cup (240 ml) low-sodium chicken broth into the bottom of the 6-quart (5.7 L) slow cooker. Arrange the seasoned turkey drumsticks over the broth, placing the thicker ends toward the outer edges when possible. A little overlap is acceptable, but avoid tightly packing the meat. Allow approximately 3 minutes for arranging. The broth should remain visible at the bottom rather than completely covering the turkey.

Cover the slow cooker securely and select the LOW setting. Cook for approximately 7 hours, keeping the lid closed to maintain consistent heat and moisture. By the end of cooking, the drumsticks should look fully cooked, with softened skin and meat that yields easily when pressed with tongs. The liquid should be gently bubbling around the edges. Cooking time can vary with drumstick size and slow cooker performance.

Near the end of the 7-hour cooking period, insert an instant-read thermometer into the thickest portion of each drumstick without touching the bone. The turkey must reach at least 165°F (74°C) for food safety. For a more tender, easily separated dark-meat texture, a temperature around 175–185°F (79–85°C) is often desirable. If the meat is still firm, continue cooking on LOW, checking periodically until it becomes tender and reaches the required safe temperature.

Use kitchen tongs to transfer the cooked drumsticks carefully to a large serving platter. Let them rest for 10 minutes before serving. During this period, carryover heat and moisture redistribution help the meat retain its juices. The turkey should remain moist, and the meat should separate from the bone easily when pulled with a fork.

After the 10-minute rest, use a ladle or serving spoon to collect some of the warm cooking liquid from the slow cooker. Skim off excess surface fat if needed, then spoon the juices over the turkey immediately before serving. The liquid should be savory and lightly colored by the paprika, with visible herbs and natural turkey juices. Serve while hot.