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Preheat the oven to 325°. Spread the blanched almonds in a pie plate or on a small baking sheet. Bake the almonds for 8 minutes, or until lightly toasted. Transfer the toasted almonds to a plate and let them cool completely. Lightly oil a 9-inch round springform pan.
Finely grate 1 1/4 teaspoons of the zest from the orange. In a food processor, pulse the toasted almonds with the confectioners' sugar until the nuts are finely ground. Add the flour, 3/4 teaspoon of the orange zest and the salt, then pulse the mixture until combined. Add the cold butter and pulse just until the mixture resembles large crumbs; stop pulsing before the dough begins to clump together. Add the orange-flower water or vanilla extract and pulse just until the dough forms large clumps.
Scrape the shortbread dough into the prepared springform pan. Using floured hands, press the dough into an even layer and prick it all over the top with a fork. Bake for about 25 minutes, or until the shortbread is golden brown around the edges; rotate the pan halfway through baking for even browning.
Transfer the pan to a wire rack and immediately cut the shortbread into 12 wedges. Let the shortbread wedges cool in the pan.
Meanwhile, with a sharp knife, peel the orange, removing all of the bitter white pith. Working over a medium sauce-pan, cut in between the membranes to release the orange sections into the saucepan. Squeeze the juice from the orange membranes into the pan. Add the sliced strawberries, granulated sugar and the remaining 1/2 teaspoon of orange zest and bring to a simmer.
Cook the fruit over moderate heat, stirring occasionally, until the strawberries and oranges are softened and syrupy, about 8 minutes. The fruit compote should be slightly thinner than jam. Transfer the compote to a bowl and let cool to room temperature.
Remove the springform ring and arrange the shortbread wedges on plates. Serve with the strawberry compote and the crème fraîche.
The shortbreads can be stored in an airtight container for up to 2 days. The compote can be refrigerated for up to 2 days.