In a large bowl, using a hand mixer, beat the shortening, sugar, eggs, milk and vanilla extract together until smooth, about 1-2 minutes.
1 cup vegetable shortening, 1 cup granulated sugar, 2 large eggs, 2 tablespoons milk, 1 tablespoon pure vanilla extract
In a separate bowl, stir together flour, baking powder, and salt.
3½ cups all-purpose flour, ½ teaspoon kosher salt, 2 teaspoons baking powder
Add dry ingredients to wet ingredients and beat just until well combined and the dough starts to stick together, about 1–2 minutes. Do not overmix.
Line a baking sheet with parchment paper. Set aside.
Sprinkle a clean work surface lightly with flour, then place about ⅓ of the dough onto the prepared surface to roll out. Sprinkle the top of the dough with flour to prevent the dough from sticking to the rolling pin.
For soft and thick cookies, it’s recommended to use a rolling pin with thickness rings and use the ⅜-inch thickness ring. If you aren’t cutting these cookies out thick, you’ll want to reduce your baking time to reflect that (start checking cookies after 8 minutes instead of 12 minutes).
Cut the cookies out using egg-shaped cookie cutters. The eggs shown here are about 3 inches in size, but slightly larger works just fine.
Place the cut-out cookies onto the prepared baking sheet. The cookies can be placed close together on the baking sheet for this step. Place sugar cookies in the freezer for 20 minutes to chill before baking.
While the cookies chill, preheat oven to 350°F.
Line a second baking sheet with parchment paper. Place some cookies onto the baking sheet (about 2 inches apart) and bake for 12-14 minutes for thick-cut cookies, 8-10 minutes for thinner cookies, or until tops of cookies look set (no longer wet but not yet brown) and the bottoms of cookies are slightly brown. The middle of cookies will still be slightly soft to the touch but will continue baking once removed from the oven. Only bake one tray of cookies at a time to ensure even baking time for all cookies.
Repeat baking steps with remaining cookies.
Let cookies cool completely before frosting.