For the pasta frolla, combine the flour, sugar, and salt in a mixing bowl. Stir well to mix. Remove the butter from the refrigerator, unwrap, and place on a work surface. Pound it gently with a rolling pin or the heel of your hand to make it pliable. After 3 or 4 strokes, the butter should have softened sufficiently. Use a scraper to remove it from the work surface, and add it to the bowl with the flour mixture.
Toss the piece of butter to coat it with flour and break it up into 6 or 8 pieces, using your fingertips. Continue breaking the butter into smaller pieces and rubbing it into the flour mixture with your fingertips. At the same time, work the flour mixture upward from the bottom of the bowl so that it mixes evenly with the butter. The whole process should take no more than 2 minutes. Work quickly to make sure that the mixture remains cool and powdery and does not become pasty, which would be a sign that the butter is melting and that the resulting dough will be tough.
Break the egg into a small bowl or cup, beat it lightly with a fork, and stir into the butter-flour mixture. Continue stirring with the fork until the dough begins to hold together.
Empty the contents of the bowl onto a lightly floured work surface and squeeze the dough together gently until it is smooth, very briefly, without overworking it. Shape the dough into a thick disk, about 4 inches in diameter, and wrap in plastic. Chill the dough until needed. It may be prepared up to 3 days ahead.
For the almond filling, break the almond paste into 1-inch pieces and place in the bowl of a heavy-duty mixer fitted with the paddle or in a food processor fitted with the metal blade. Add one yolk and mix on the lowest speed or pulse in the processor. After the first yolk is almost absorbed, add the second and beat or process until smooth. Add the last yolk and the liqueur and work until smooth again. Cover the filling until assembling the pastries, to prevent it from forming a crust. To assemble the pastries, first roll the dough out into a 4 × 12-inch rectangle and drape it over twelve 3- to 4-inch barquette pans arranged in a double row. Press the dough well into the pans, then roll over with the rolling pin to cut away any excess dough. Arrange the pans on a cookie sheet and chill them until the dough is firm, about 1 hour.
To fill the pastries, place the filling in a pastry bag fitted with a ½-inch star tube (Ateco #4). Pipe the filling in the form of a large spiral, as in the illustration. Fill all the lined pans. Bake the pastries at 375 degrees for about 20 minutes, until the filling is firm and well colored and the dough is baked through.
While the pastries are baking, prepare the glaze: combine the corn syrup and vanilla in a small saucepan and heat until bubbles form around the edges. Immediately after removing the pastries from the oven, brush them with the hot glaze. Cool in the pans before unmolding.