Heat heavy cream and honey in a 1-quart heavy-bottomed saucepan over medium-high heat until bubbled begin to form.
Place chopped chocolate in a medium-sized mixing bowl.
Add half the hot cream to chocolate, let mixture stand for about 30 seconds undisturbed, then stir lightly to combine. Repeat with remaining cream, then stir the resulting ganache gently until all chocolate has melted and mixture is smooth. Add butter, and whisk until well blended.
Fill shell with ganache, transfer to a baking sheet, and refrigerate until filling is set (about 1 1/2 hours). When ready, remove tart from refrigerator, and serve.