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Preheat your oven at 400°F one hour before you want to bake your galette. If you have one, place a baking stone or baking steel on the rack in the middle of the oven. If not place a large sheet pan, rim side down on the oven rack. It will act like a baking stone and create a hot surface for the galette crust to get crisp.
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Cover a rimmed sheet pan, large enough to hold a 10-inch (25 cm) galette, with parchment paper. Set aside.
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Take the galette dough out of the refrigerator and rest it on the counter for 10 minutes. Lightly sprinkle flour over your clean work surface and unwrap your dough. Lightly flour your rolling pin and give your dough a few good whacks with the pin to soften it up. Turn over the dough and repeat. Repeat whacking the dough several turns to help shape the dough in a circle and thin it out.
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Roll the dough into a 12 inch (30.5 cm) circle. Start with the pin across the middle of the dough and roll the pin away from you. Return the pin to the middle and roll the pin towards you. Turn your galette dough 1/8th turn and repeat, rolling the dough, starting each time at the middle of the dough and roll once away, then once toward you. Repeat until you have a circle about 12- inches (30.5 cm) across and 1/4-inch (.33 - .5 cm) thick. You should get a nice shaped circle with this method. If the dough needs thinning and shaping, move your pin over to those areas roll the pin in one direction at a time.
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Transfer your finished galette dough to your prepared sheet pan. Place your rolling pin across the middle of your pie dough, and drape the top half of the dough over the pin towards you. Lift the pin and place it across the middle of your sheet pan and arrange the galette dough flat on the baking sheet. Cover loosely with plastic wrap and refrigerate for 30 minutes to an hour.
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Assemble the galette. Place the baking sheet with the chilled galette dough on your counter. Spread the prepared almond paste across the middle of the galette dough making a circle about 9 inches (23 cm) across. Add the peaches to the galette dough by one of two methods. One- carefully arrange the peach slices in a circle around the dough, beginning 2-3 inches from the edge of the dough. Make and fill a circle with the peach slices. Make sure you overlap the slices because they will separate while baking. Add the pitted cherries into pockets of the peaches any which way you want. Or, two- add the cherries to the bowl with the peaches and dump the fruit in the center of the galette dough. Smooth the peaches out to make a nice mound over the almond paste.
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Fold the edge of the dough over the fruit and pleat and pinch the folds together, creating a nice and neat package.
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Chill the galette for 30 minutes, loosely covered with plastic wrap. This will help the galette dough keep its shape. Or, bake right away but the galette might open slightly.
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Just before baking, baste the folded galette dough with an egg wash, and sprinkle the dough with the course or granulated sugar. Brush away any loose sugar from the galette on the baking sheet. Scatter pieces of the butter over the peaches and sprinkle with some more sugar.
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Place the baking sheet with the galette in the oven and bake for 40 - 45 minutes, or until the crust is golden brown and the juices are vigorously bubbling.
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Remove the baking sheet with the galette from the oven and set on a cooling rack to cool. Galettes should be set and completely cooled before eating. This can take a couple of hours. When completely cooled, carefully slide the galette onto your serving plate using the parchment paper to help you. If you have any leakage, run a large spatula or knife, under the galette to loosen any stuck sections.
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Serve room temperature.