In a food processor, combine gluten-free flour, granulated sugar, baking powder, and kosher salt. Add cold butter and cream cheese. Pulse until coarse crumbs form, about 15-20 seconds. Slowly add milk and vanilla, pulsing until dough comes together, about 10 seconds.

Transfer the dough to a floured surface, shape into a rectangle about 1 inch thick. Wrap in plastic wrap and refrigerate for 10-15 minutes.

Roll out the chilled dough to ¼ inch thick. Fold into thirds like a letter, wrap and refrigerate for another 10-15 minutes. Repeat rolling and folding three times.

While the dough chills, mix chopped chocolate, cocoa powder, brown sugar, and salt in a bowl.

Roll the laminated dough into a large circle. Brush melted butter over it, sprinkle chocolate filling mixture evenly. Roll the dough into a tight log.

Cut the log into 1.5-inch segments and place on a parchment-lined baking sheet. Chill in the refrigerator for at least 1 hour.

Preheat oven to 400°F. Prepare an egg wash by whisking an egg with water. Brush over the tops of chilled rugelach.

Bake in the oven at 400°F for 10 minutes, then reduce to 375°F for an additional 20-24 minutes until golden brown.

Remove from oven and let cool on a wire rack for about 10 minutes before serving.