1. Place horehound tea leaves in a medium heatproof glass bowl. Bring 2 cups water to a boil. Pour over leaves; let steep 3 minutes. Strain liquid into a 2-cup liquid measure; add enough water to total 2 cups. Line a baking pan with a Silpat (a French nonstick baking mat). Set pan aside.

2. Heat oven to 350 degrees. In a large saucepan set over medium-high heat, combine the tea, sugar, and corn syrup. Stir to dissolve. Cook until a candy thermometer registers 280 degrees, about 35 minutes.

3. Remove pan from heat; stir in peppermint oil. Pour three 12-inch-long strands onto baking mat. Allow mixture to cool slightly, 2 to 3 minutes. When cool enough to handle, roll each strand into a slender cylinder, about 1/2 inch in diameter. Let cool slightly, about 1 1/2 minutes. Place cylinders on a cutting board, and cut into 3/4-inch-thick pieces.

4. Return the pieces to the baking mat. Place in oven to soften, about 2 minutes. Roll pieces into balls, and flatten slightly with your fingertip, forming lozenges. If balls harden during process, return pan to oven to soften. Wrap the lozenges individually in cellophane or store on sheets of parchment in an airtight container up to 3 weeks.