For variations on these cookies, try adding lemon zest, dipping them in chocolate, or sandwiching two of them together with jam.
Cut two pieces of parchment or waxed paper into 12-by-20-inch rectangles. Set aside. In the bowl of a heavy-duty electric mixer fitted with the paddle attachment, mix together butter, confectioners' sugar, and 1 1/2 tablespoons granulated sugar on medium-low speed. Add vanilla extract; mix until just combined.
In a medium bowl, whisk together salt and flour. With mixer on low speed, gradually add the flour mixture to the butter mixture. Mix dough, scraping down sides of bowl once or twice, until just combined.
Transfer dough to center of one of the reserved pieces of parchment paper. Place second piece of reserved parchment paper directly over dough. Shape dough into a round. On a flat surface, roll dough to 1/8-inch thickness. Chill until firm on a baking sheet, about 1 hour.
Heat oven to 325 degrees. In a small bowl, whisk egg together with 1 teaspoon cold water. Set aside. Line two baking pans with Silpats. Set aside.
Remove chilled dough from refrigerator, and place on a flat surface. Remove parchment paper from surface of dough, and reserve. Using a 3 1/2-inch round cutter, cut out dough rounds, and transfer to prepared baking pans; space rounds about 2 inches apart. Lightly brush cookies with egg wash, and decorate with three sliced almonds.
In a small bowl, combine remaining 2 tablespoons sugar with cinnamon. Sprinkle over cookies.
Bake until light golden brown, 15 to 20 minutes. Transfer cookies to a wire rack to cool.
Reroll remaining dough between reserved parchment to 1/8-inch thickness, and chill until firm, about 1 hour. Repeat steps 5, 6, and 7 with chilled dough.