Freeze cubed butter for 30 minutes.

In the work bowl of a food processor, place 2¼ cups (281 grams) all-purpose flour and 2 teaspoons (6 grams) salt; pulse until combined. Add frozen butter; pulse until butter is dime-size. With processor running, add ½ cup (120 grams) ice water in a slow, steady stream just until mixture forms a ball. Turn out dough onto a lightly floured surface; shape into a 6-inch square. Wrap in plastic wrap, and refrigerate for at least 30 minutes.

On a lightly floured surface, roll dough into a 15×7-inch rectangle, lightly flouring surface as needed to prevent sticking. Fold dough in thirds, like a letter, and rotate 90 degrees. Repeat procedure twice. Wrap in plastic wrap, and refrigerate for at least 20 minutes.

Line 2 baking sheets with parchment paper.

Divide dough in half. On a lightly floured surface, roll one half into a 12×9-inch rectangle (about ⅛ inch thick), lightly flouring surface and dough as needed to prevent sticking. Using a 4-inch round cutter, cut 5 circles. Place 2 inches apart on a prepared pan. Repeat procedure with remaining dough.

In a small bowl, stir room temperature butter until creamy. Add almond flour, sugar, 1 egg yolk (19 grams), almond extract, remaining 1½ teaspoons (4.5 grams) all-purpose flour, and remaining ⅛ teaspoon salt; stir until well combined.

Using the tines of a fork, dock 5 dough circles all over. Spread 2 tablespoons (about 30 grams) frangipane on each docked circle, leaving a ½- to ¾-inch border around edges. Place whole almond (if using) in frangipane on 1 circle. Brush dough edges with room temperature water. Top with remaining dough circles, lining up edges and pressing down to seal with bottom circles. Refrigerate for 30 minutes.

Preheat oven to 400°F (200°C).

In a small bowl, whisk together 1 teaspoon (5 grams) room temperature water and remaining 1 egg yolk (19 grams).

Using your fingertip, press down dough edge; using the back of a small knife, simultaneously make a notch just to the side of your fingertip as if marking its location. Move fingertip to other side of notch, and repeat procedure all the way around edge. Repeat with remaining galettes. Score desired design on top of each galette. Brush tops with egg wash, being careful not to let egg wash drip down sides. Cut 5 to 6 small discreet slits in scored design to allow steam to escape.

Bake for 15 minutes. Rotate pans, and reduce oven temperature to 375°F (190°C); bake until deep golden brown, 10 to 15 minutes more, re-opening slits in tops if needed. Serve warm or let cool completely on a wire rack.