Butter or line with parchment paper 2 cookie sheets.
In a large bowl beat butter and sugar until creamy, 1 or 2 minutes.
Add eggs, half of the milk and vanilla and mix until combined.
Add dry ingredients, flour, cornstarch, baking powder and salt.
Mix a bit and then add some or all of the rest of the milk until you have a dough that can hold and be scooped. Sometimes I don’t use the full amount of milk.
Drop teaspoonfuls or small scoops of dough a few inches apart onto the baking sheets, and lightly flatten the tips with damp fingers.
Bake for 12-15 minutes, depending on the size, but check for doneness after 10 minutes. They should’ve risen slightly and start to barely color on the edges.
Let cool completely on wire racks.
For the white glaze:
Mix all ingredients until smooth.
For the chocolate glaze:
Melt chocolate or chips and butter (in the microwave or over a bowl of hot water not touching the bottom of the bowl).
Mix in the syrup and salt and mix until creamy.
Glaze each half cookie with one of the glazes, spreading them with the back of a spoon or a small spatula.