Step 1

To make the dough: In a large bowl, beat together the shortening, butter, sugar, and cream cheese until smooth. Beat in the egg and vanilla. Add the spices, baking soda, salt, and flour and mix until the dough comes together. Divide the dough into quarters and place on pieces of parchment. Roll the dough 1/2" thick. Stack the pieces of dough (on their parchment) on a baking sheet, cover with plastic (or your favorite reusable wrap), and refrigerate for at least 1 hour.

Step 2

, To cut and bake: Preheat the oven to 375°F. Line two baking sheets with parchment.

Step 3

, Lightly flour your work surface and work with one piece of dough at a time. Roll the dough 1/4" thick and cut into desired shapes; re-roll the scraps and cut additional shapes. This dough is quite forgiving; scraps can be gathered and re-rolled up to three times before getting tough. Transfer the cookies to the prepared baking sheets.

Step 4

, Bake the cookies for 7 to 9 minutes, until the edges just begin to brown. Remove from the oven and let cool on the pan for 5 minutes before transferring to a rack to finish cooling completely.

Step 5

, To make the glaze: Whisk together the confectioners’ sugar, corn syrup, vanilla, and 3 tablespoons of the milk in a medium bowl; the mixture should be thick. Add more milk a teaspoon at a time, until the glaze is the consistency of honey. It should fall off the spoon in a thick ribbon that disappears back into the bowl after a few seconds. Use to glaze the cooled cookies.

Step 6

, Storage information: Store cookies airtight at room temperature for up to 3 weeks; freeze for longer storage.