Cream together the butter and sugar until smooth then stir in remaining cookie ingredients.
For each cookie, roll 2 teaspoons dough into a ball, then indent a hole with the end of a wooden spoon.
Place on a parchment lined baking sheet and bake for ten minutes.
Remove from oven and improve the hole again with the spoon (in case it filled in).
Fill the hole with about 1/2 teaspoon ja, more or less, but do not overfill.
Bake cookies 8 minutes more then allow to cool.
Whisk together the confectioner's sugar, vanilla and half and half, adjusting the amount of milk so that it has a good drizzling consistency that thinly pours out of a small spoon.