Combine 1/2 cup honey, 1/2 cup sliced peeled ginger, and 1/2 cup water in a small saucepan. Bring to a simmer over medium heat and cook, stirring occasionally, until flavours meld, about 15 minutes. Remove from heat and let cool.

Strain syrup into a large pitcher. Add 4 cups club soda, fresh mint, and ice. Stir gently and divide among 8-ounce glasses.