In a large bowl, combine the almond flour, powdered erythritol, and salt. Add the softened butter and work it in with a fork or your fingers until the mixture looks crumbly.
Add the egg, vanilla extract, and almond extract. Stir until a cohesive dough forms. Wrap the dough in plastic wrap, flatten into a disc, and refrigerate for 30 minutes.
Preheat oven to 325°F (165°C) and line a baking sheet with parchment paper. Roll the chilled dough between two sheets of parchment to about 1/4 inch thickness.
Cut out shapes with cookie cutters and carefully place them on the prepared baking sheet, spacing about 1 inch apart. Re-roll scraps and cut more cookies.
Bake for 10 to 13 minutes, until the edges are just barely golden. The centers will still look soft. Let them cool completely on the baking sheet before frosting.
While the cookies cool, make the frosting. Beat the cream cheese and butter together until smooth. Add the powdered erythritol and vanilla, then beat on medium-high until light and fluffy, about 2 minutes.
Spread or pipe the frosting onto the fully cooled cookies. Let the frosting set for 15 minutes before stacking or serving.
