Add the honey, grated ginger, lemon juice, turmeric, cinnamon, and black pepper to a small saucepan.
Heat over medium-high heat, stirring constantly with a silicone spatula and scraping the sides of the pan.
Continue cooking until the mixture reaches 300°F (hard crack stage), watching closely to prevent burning.
Remove from heat immediately.
Carefully pour the hot mixture into silicone molds, or spoon small drops onto parchment paper dusted with arrowroot powder or powdered sugar.
Let the cough drops cool and harden completely at room temperature.
Dust the finished cough drops with a 1:1 mixture of arrowroot powder and powdered sugar.
Store in an airtight container at room temperature.