Make the frangipane. In a small mixing bowl, beat the softened butter and 1/3 cup granulated sugar together with a fork until smooth and creamy, about 1 minute. Add the egg and almond extract and stir until combined. Fold in the almond flour, all-purpose flour, and salt. The filling will be thick and slightly sticky, similar to a soft cookie dough. Cover and refrigerate while you prepare the dough and pears.

Peel and core the pears, then slice them thin, about 1/8 inch thick. Toss them with the lemon juice in a bowl so they do not brown while you work.

On a lightly floured surface, roll out one pie dough round until it is about 1/8 inch thick. Use a 5 to 6-inch round cutter or the rim of a bowl to cut out circles. Gather and re-roll scraps as needed. You should get 8 circles total from both rounds of dough. Keep the cut circles on a parchment-lined baking sheet in the refrigerator while you work.

Working with one circle at a time, spoon about 1 heaping tablespoon of frangipane into the center of the dough. Spread it out gently, leaving about a 3/4-inch border around the edge. Layer 3 to 4 thin pear slices on top of the frangipane, arranging them in a small fan or overlap so they lay flat.

Brush the border of the dough circle lightly with egg wash, then fold one half of the circle over the filling to form a half-moon shape. Press the edges together firmly with your fingers, then crimp with a fork all the way around to seal. Place the finished pie back on the parchment-lined baking sheet and repeat with the remaining dough and filling.

Once all 8 pies are assembled, slide the baking sheet into the refrigerator and chill for 15 minutes. This helps the dough firm back up so the pies hold their shape and bake with a flakier crust.

Preheat your oven to 400 degrees F. Remove the pies from the refrigerator. Brush the tops with egg wash and use a sharp knife to cut 2 small slits in the top of each pie to let steam escape. Sprinkle coarse sugar over the tops if using.

Bake for 20 to 24 minutes until the pies are deeply golden brown all over. Pale golden is not enough here. You want real color for the best texture and flavor. Let them cool on the pan for at least 10 minutes before eating. The filling will be very hot straight from the oven.