1/2 cup packed canned almond paste* (about 5 oz; not marzipan), coarsely crumbled
1/2 tsp. salt
3/4 cup sugar
2 sticks (1 cup) unsalted butter, softened
1 large egg, separated
1 tsp. almond extract
1 1/4 cups flour
1/2 cup sliced almonds (about 1 1/2 oz.)
Pulse almond paste in a food processor until broken up into small bits, then add salt and 1/4 cup sugar. Continue to pulse until finely ground, about 1 minute.
Put oven rack in middle position and preheat oven to 350 degrees. Butter a 9-inch-square baking pan and line with foil, leaving a 2-inch overhang on two opposite sides. Butter foil.
Beat together butter and remaining 1/2 cup sugar in a large bowl with an electric mixer at medium-high speed until pale and fluffy, about three minutes in a stand mixer with a paddle attachment or six minutes with a handheld. Add almond mixture, egg yolk and almond extract and beat until combined well, about two minutes. Reduce speed to low, add flour and mix until combined.
Spread batter evenly in pan with an offset spatula. Lightly beat egg white in a small bowl, then brush some of it over batter and sprinkle evenly with almonds.
Bake until top is golden, 35 to 40 minutes. Cool completely in pan on a rack, about an hour. Transfer with foil to a cutting board, then discard foil. Cut into squares or decorative rounds using a crimp-edge 1- or 2-inch cookie cutter.