With a tender crust, sweet-tart apricots, and a creamy almond filling, this rustic galette is my take on a classic French dessert. Because it's quite delicate I recommend serving it directly from the baking sheet. Begin your prep several hours in advance to give the dough a chance to chill and the finished tart an opportunity to cool completely.
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In the bowl of a stand mixer fitted with the paddle attachment, mix the flour, almond meal, salt, sugar, and cold butter on low speed until clumps begin to form, about 1 minute. Add the almond extract and ice water and continue mixing until the dough comes together in a mass, 1-2 minutes longer.
Transfer to a large sheet of plastic wrap, flatten into a 4 1/2-inch disc, wrap tightly, and refrigerate for 1 hour.
Beat the almond meal, sugar, butter, egg yolk (reserve the egg white), almond extract, and salt on medium speed in the same mixing bowl (no need to clean it) until smooth, about 1 minute. Refrigerate, covered, until the crust is ready.
Line a heavy rimmed baking sheet parchment. (If your baking sheet is thin, stack two together.)
In a large bowl, toss the apricots with the sugar and lemon juice. On a floured countertop, roll out the chilled dough to a rough 11-inch circle. Transfer to the prepared baking sheet. Spread the frangipane thickly over the dough, leaving a 1 1/2-inch border. Scatter the apricots cut-sides down atop the frangipane, scraping any residual juices on top. (Do not pile the apricots in a heap. If they don't fit, eat them separately.) Fold in the pastry, pleating as you go, leaving a 4-5 inch circle of fruit exposed. Freeze on the baking sheet for 20 minutes.
Meanwhile, preheat the oven to 450 degrees. Whisk the reserved egg white until frothy. Brush it on the exposed pastry. Bake in the center of the oven for 25-30 minutes, or until the pastry is golden brown and the frangipane is set. Transfer the baking sheet to a cooling rack. Allow the galette to cool to room temperature, at least 30 minutes. Slice and serve directly from the baking sheet.