Place dough on a lightly floured work surface; cover and let stand until butter is slightly softened, 5 to 10 minutes.
Roll dough out to a 10-by-18-inch rectangle. Cut rectangle in half crosswise. Wrap one half with plastic wrap and transfer to refrigerator. Place remaining half on a large (about 18-by-25-inches) piece of parchment paper. Roll into a 16-by-20-inch rectangle, stopping to chill dough as necessary if butter becomes too soft; transfer to a large baking sheet and cover with plastic wrap. Transfer baking sheet to refrigerator and chill until firm, about 30 minutes. Repeat process with remaining piece of dough.
Transfer one piece of dough to a lightly floured work surface so that one of the longer sides is facing you. Halve dough lengthwise to make two 8-by-20-inch rectangles.
Using a pizza cutter, trim a scant 1/8 inch from top and bottom of each rectangle of dough. Working quickly, use the pizza cutter to mark 5-inch increments along the bottom (side closest to you) edge of each dough half. Working from left to right, measure 2 1/2 inches on top of each half and make a mark using the pizza cutter. Continue along the top edges marking at 5-inch increments until you reach the end of the dough.
Using a ruler, cut dough into triangles with a 5-inch base, Discard scraps. You should have 14 triangles. Gently stretch triangles to make them 1 1/2 times their length. Roll 1/4-inch pieces almond paste into narrow log and place one piece at the base of each triangle.
Working with 1 triangle of dough at a time, place dough triangle on work surface so that the point is furthest from you. Starting at the base, gently roll dough away from you, stretching the point as you go, with fingers or a rolling pin; secure point underneath roll. Curve ends away from you to make a crescent shape.
Line baking sheets with parchment paper; place 4 crescents on each prepared baking sheet. In a small bowl, whisk egg with 1 teaspoon water. Brush tops of crescents with egg mixture, reserving remaining egg mixture. Place 3 narrow drinking glasses upside-down between crescents; cover well with plastic wrap, making sure plastic does not touch dough. Let stand in a warm place until doubled in size and crescents feel hollow when gently touched, 2 1/2 to 3 hours.
Preheat oven to 425 degrees.
Uncover and remove glasses from baking sheets; brush croissants lightly with remaining egg mixture (reserving remaining for second piece of dough). Transfer to oven and bake until puffed and golden, about 15 minutes. Transfer to a wire rack to cool. Repeat steps 3 through 9 with remaining piece of refrigerated dough.