Dust a clean, dry surface with a small amount of flour (take a pinch between your fingers and then throw it onto the countertop like you were shooting dice). With a rolling pin, roll the pate sablee using quick, short strokes from the middle of the dough, until you've formed a circle roughly 10-inches in diameter and about 1/4-inch thick. Every few strokes, lift and turn the dough a quarter-turn, dusting underneath with a small amount more of flour, if necessary, to prevent sticking. Place your rolling pin over the bottom quarter of the dough and lift the bottom edge of the dough up and over the pin. Roll the pin away from you slightly to help gather the dough circle onto the pin, then unroll the dough onto a parchment paper lined baking sheet. Place the baking sheet in the refrigerator to chill for 10 minutes and up to 30 minutes.
Preheat the oven to 350 degrees F.
Place the plum wedges in a bowl and toss with the sugar and juice of half a lemon. Remove the baking sheet from the freezer. Working from the center, arrange the plum wedges thickly over the dough, leaving about a 1 1/2-inch border all around the edges. Fold the exposed edges of dough up and over the plums so that the galette looks something like a pizza with a border of crust all around the outside. Brush the dough with the beaten egg and sprinkle with more sugar. Place on the bottom rack of the oven and bake until the crust is golden and the fruit is soft, about 1 hour. Remove from oven and allow to cool slightly on a baking rack. If using, sprinkle with the toasted almonds.
When the galette is no longer hot to the touch, slide onto a cake plate or pedestal. Serve warm or at room temperature.
In the bowl of a food processor, combine the flour, sugar, and salt. Pulse to combine. Add the butter and pulse the food processor on and off until the mixture resembles coarse sand with pea-sized lumps of butter still showing. Add the egg yolk and the ice water and pulse on and off until the mixture comes together but does not form a single mass. Turn the dough out onto a clean surface and gather it up into a loose ball. Working with a small bit of dough at a time, smoosh the dough across the counter away from you with the heel of your hand and then scrape it up with a pastry cutter and gather it back together, forming a second ball. Repeat with the remaining dough until all the smooshed dough is in a single ball. Flatten into a disk, wrap well in plastic wrap, and let rest in the refrigerator at least 30 minutes and up to overnight.