For the honey syrup: In a small saucepan, heat the honey with 1/3 cup water until it just comes to a simmer. Cool completely.
For the gold rush cocktail: Place 1 large ice cube in each of 4 rocks glasses. Combine the bourbon and lemon juice in a cocktail shaker with 1/2 cup honey syrup and some ice. Shake and strain into the glasses, garnish with the mint and serve.