Make sugar cookies
Whisk all purpose flour, cake flour, baking powder and salt in a large bowl, set aside.
In the bowl of a stand mixer, with paddle attachment, combine butter and sugar. Beat on medium speed until fluffy and light in color, about 5 minutes. (If using a hand mixer about 7 - 8 minutes.)
Add the eggs and beat on medium speed until incorporated, then add the vanilla and beat until mixture is uniform.
Add flour mixture in two batches, alternating with the cream, and mix until just combined.
Divide the dough into thirds and roll out to 1/4" thickness between 2 sheets of parchment paper. (You'll have 3 pieces of dough, you'll need 6 sheets of parchment)
Put the sheets of dough (and the paper!) on a sheet pan to keep them flat, then freeze for an hour until dough is very firm.
Dip cookie cutter in flour, then cut out shapes and place them on a baking sheet lined with a silicone baking mat or parchment paper. Freeze the dough for a minimum of 2 hours. (I wrapped my sheet pans up and froze overnight).
Preheat oven to 325°F with convection or 350°F without convection.
Remove sheet pan from freezer and bake for 18 minutes. (This is for 3 inch cookies. If your cookies are smaller or larger, adjust the time by a minute or two)
Let cool on baking sheet for a few minutes before transferring to rack to cool completely.
Make icing & dip cookies
Stir powdered sugar, water (or vodka), corn syrup, vanilla and salt together in a bowl wide enough to fit your largest cookie.
Test icing for consistency (see note) and adjust if necessary.
Add 3 - 4 drops of gel color and swirl with a toothpick or wooden skewer.
Hold cookie above icing bowl and gently dip straight down, then pull up and tip cookie to let excess icing run off the side. Tip in the opposite direction to let icing settle. (This will also give you a better marbling effect)
Place cookies on baking sheet to let the icing harden for at least 6 - 8 hours, up to 24 hours.