For cookies: In a large bowl, combine butter, brown sugar, and honey. Stir until creamy. Beat in the egg and vanilla until smooth.
Sift the dry ingredients over the butter mixture and stir until incorporated.
Turn the dough out onto a lightly floured work surface and knead once or twice. Divide the dough in half. Flatten each half into a 1-inch-thick disk. Wrap and refrigerate for at least 2 hours, or overnight.
Preheat oven to 350°F. Lightly grease two baking sheets.
Roll one piece of the dough ¼-inch thick on wax paper. Cut out shapes and place on the prepared cookie sheets. Repeat for the remaining dough and scraps.
Bake for 14 to 18 minutes, or until golden. Cool briefly on the baking sheets, then transfer to a rack to cool.
For frosting: Combine all of the ingredients in a small bowl and beat with a fork until smooth.
Decorate the cookies with frosting. Allow the frosting to dry before stacking cookies.