Preheat oven to 350F
In a small bowl or jug, whisk together the egg, milk, vanilla and nutmeg. Remove 3tbsp from the mixture and set it aside, refrigerated, for later.
Cream together the butter, sugar and honey. Add the remaining egg-milk mixture, flour and baking soda. Mix until well combined but try not to overmix (this can all be done in food processor/stand mixer).
Take spoonfuls of the mixture, approx 1tbsp size, and place on a cookie sheet/lined baking sheet/tray with a bit of space between them. Try to smooth the sides a little (they will melt down a little as they cook but they won't become flat).
Bake in the preheated oven for approx 12 minutes until just turning brown. Allow to cool completely.
As the cookies cool, cream together the 1tbsp butter, confectioners sugar and 1tsp of the egg-milk mixture you saved earlier. Blend until smooth then drizzle this frosting over the cooled cookies. Allow to harden up. The cookies will keep refrigerated in a sealed container for a couple days.