Make the syrup: Combine the tea and honey in a small saucepan over medium-low heat. Reduce until syrupy, about 10 minutes, then let cool.
Make the cocktail: Combine 1/2 ounce tea syrup, 2 sage leaves, the Peychaud's bitters and orange juice in a cocktail shaker. Gently muddle the sage with a muddler or the handle of a wooden spoon. Add the rye and Averna and fill the shaker three-quarters of the way with ice. Give it a short shake, then strain into a martini glass and garnish with the remaining sage leaf.
Photograph by Jonathan Kantor
Recipe adapted from Clock Bar (San Francisco) for Food Network Magazine