How to Make It
In a food processor, pulse the flour with the butter until the mixture resembles coarse meal. Add the ice water and pulse just until the dough comes together. Divide in half and press into disks. Wrap in plastic and refrigerate until firm, at least 1 hour or overnight.
Meanwhile, in a stand mixer fitted with the paddle, beat the almond paste with the egg white, both sugars, vanilla and cardamom at medium speed until smooth, about 4 minutes. Spoon the spiced almond paste into a pastry bag fitted with a 1/2-inch tip or use a sturdy, resealable plastic bag and snip off a corner.
Line 2 baking sheets with parchment paper. In a small bowl, lightly beat the egg with the milk. On a lightly floured surface, roll out 1 disk of dough into a 14-by-8-inch rectangle. Cut the dough crosswise into eight 1 3/4-inch strips.
Pipe a line of almond paste down the center of each strip. Brush one side of each strip with the beaten egg. Roll one side over the filling and pinch the seam closed. Transfer the logs to one of the prepared baking sheets seam side down. Form each log into an S shape. Repeat with the remaining disk of dough, almond paste and beaten egg. Freeze the cookies until firm, about 1 hour.
Preheat the oven to 375°. Brush the cookies with the remaining beaten egg and sprinkle with fleur de sel. Bake for 20 to 25 minutes, until golden. Transfer the cookies to a wire rack and let cool slightly. Serve warm or at room temperature.