Whisk flour, baking powder and salt in a medium bowl.
In a large bowl, cream butter, Crisco and sugar until light and fluffy. Beat in eggs one at a time, making sure each is fully incorporated. Mix in vanilla.
On low speed, gradually blend in dry ingredients until just combined. Cover and chill in the refrigerator for at least one hour.
Roll out half of the chilled dough onto a floured surface until an 1/8 inch thick. Keep the rest of the dough in the refrigerator until you're ready for it. Use cookie cutters to cut out shapes and transfer them onto a baking sheet lined with parchment paper or a silicone baking mat. Don't put more than 12 cookies on a pan.
Re-roll the scraps until you've used up the dough and then roll out the remaining chilled dough.
Chill each sheet of cookies for at least 30 minutes before baking. Preheat the oven to 375°F (190°C), and then bake the cookies (one pan at a time) for no more than 6-7 minutes. Don't worry if they still look a little soft when you take them out of the oven. What you don't want is for them to look wet and doughy.
Leave the cookies on the baking sheet for 5 minutes before transferring to a wire cooling rack.
Make the frosting while the cookies are cooling. Cream butter and Crisco until smooth. Mix in half of the powdered sugar on low speed. Then add milk, heavy cream, vanilla and the remaining powdered sugar. Mix on low speed until just combined, and then beat on high speed until smooth and fluffy.
Decorate as desired and store in an airtight container in the freezer.