thaw puff pastry sheets according to package directions.
Using a hand mixer on low speed, beat almond paste, the 2/3 cup granulated sugar, and eggs for the almond filling in a bowl until smooth, five minutes.
Unfold one pastry sheet on a lightly floured surface. Roll out to a 10 x 14" rectangle. Spread half of the almond filling evenly over the pastry rectangle. Sprinkle with 1/4 cup of the ground almonds.
Roll up pastry evenly from both short sides until rolled edges meet in the middle. Wrap in plastic wrap. Repeat with remaining pastry sheet, almond filling, and 1/4 cup ground almonds. Arrange wrapped rolls on a baking sheet. Freeze for at least one hour.
Preheat the oven to 350°. Line baking sheets with parchment paper.
Trim ends of cookie rolls. Cut rolls crosswise into 1/4 inch thick slices.
Arrange cookies on the prepared baking sheet, spacing cookies 1 inch apart. Refill each cookie with 1/2 teaspoon coarse sugar.
Bake cookies, one sheet at a time, until there firm to the touch and lightly browned on the bottoms, 13 to 15 minutes. Let cookies cool on the baking sheets five minutes, then transfer them to a rack. If you'd like to make them ahead and spread the filling on the pastry, roll up the pastry as directed, wrap in foil and store in the freezer for up to one month. Slice and bake as directed. Makes about 60 cookies.