Preheat the oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.
Mix together ground walnuts, sugar, 3 egg yolks, cardamom, baking soda, and rose water in a medium bowl until well blended. Roll teaspoon-sized pieces of dough into balls and place 2 inches apart onto the prepared baking sheets.
Whisk together remaining egg yolk and water using a fork. Press a walnut piece into each cookie, then brush with egg yolk glaze.
Bake in the preheated oven until golden, about 20 minutes. The cookies will appear soft and undercooked but they will harden considerably when cooled.
Remove from the oven and allow to cool on the baking sheets for at least 10 minutes before transferring to a wire rack to cool completely.