Sift the flour and baking powder into a bowl. Add the salt and set aside.
Using an electric hand mixer or a stand mixer, beat the butter and sugar on medium speed until smooth and creamy, 3 to 4 minutes. Scrape down the sides and bottom of the bowl as needed. Add the cream cheese and vanilla; mix until incorporated.
Reduce the speed to low and gradually beat in the flour mixture; beat just until incorporated and the dough starts to come together. Divide the dough into two equal pieces.
Place one piece of dough on a big, lightly floured piece of parchment paper (or a silicone mat). Lightly dust the dough with flour. Place a piece of parchment on top to prevent sticking. With a rolling pin, roll the dough out to about 1/4 to 1/8 inch (6 to 3 mm) thick. Repeat with the second piece of dough.
Place both rolled-out doughs, one on top of the other, on a baking tray, cover with plastic wrap or aluminum foil, and refrigerate for at least 2 hours and up to 2 days.
Preheat the oven to 350ºF (180ºC). Line two baking sheets with parchment paper or silicone baking mats.
Working with one sheet of dough at a time, use a cookie cutter to cut the dough into shapes. Transfer the shapes to the prepared baking sheets, spacing them about 1/2 inch apart. Gather up the dough scraps and form them into a disk, then roll out and refrigerate for 15 to 20 minutes.
Bake for 10 to 13 minutes or until the cookies are just beginning to turn brown around the edges. Remove from the oven and let them sit on the baking sheets for 5 minutes. Then use a wide metal spatula to transfer the cookies to a wire rack and let cool completely. Repeat the process to cut and bake the remaining dough.
Decorate the cooled sugar cookies as desired. If using eggless royal icing, let the icing dry completely, about 1 1/2 hours, before serving. Once the cookies have completely dried, they can be stored either in an airtight container with waxed paper in between each layer, or in an airtight bag in a single layer. You can store them at room temperature for up to 5 days.