Combine almond flour, baking powder, and vanilla extract in a mixing bowl. Add sliced cold butter and use a pastry cutter or fingertips to cut in until mixture resembles coarse crumbs.
Add softened cream cheese to the dry ingredients and mix until a shaggy dough forms. Knead briefly until smooth, then shape into a rectangle, wrap in plastic wrap, and chill for 10 minutes.
On a lightly floured surface, roll out the chilled dough into a large rectangle about 1/8 inch thick. Fold the rectangle into thirds like a letter, then turn 90 degrees, and repeat the rolling and folding process twice to create flaky layers.
Cut the layered dough into triangles using a sharp knife or pizza cutter. Roll each triangle from the wide end toward the tip to form a croissant shape, then place on a baking sheet lined with parchment paper.
Brush the croissants with beaten egg for a shiny finish and bake in a preheated oven at 350°F (175°C) for 20 minutes, until golden brown and crispy on the outside.
Remove from oven, let cool slightly, and serve warm to enjoy the layered, flaky texture with a buttery aroma.
