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1
To make the croissants, in the bowl of a stand mixer with a dough hook attachment, combine the warm water and 1/4 cup (50 g) of the sugar. Sprinkle over the yeast, and let it bloom until foamy, 5 to 10 minutes.
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2
Add the flour, remaining 1/4 cup (50 g) of sugar, milk and salt and beat on low speed until combined. As soon as all the flour is almost mixed in, mix in 1/3 cup (80 g) of the coconut oil. Turn the mixer on medium speed and knead until the dough no longer sticks to the sides of the bowl, 3 to 4 minutes. Transfer to a clean oiled bowl, cover with plastic wrap and leave it to rise for 2 hours, or until doubled in size.
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3
Punch down the risen dough to release the air. On a lightly floured surface, roll out the dough to the size of a piece of printer paper, wrap in plastic wrap and refrigerate for 1 hour. Remove from the fridge, and smear the remaining 11/3 cups (305 g) of coconut oil evenly over the middle third of the dough, then fold over the two edges to cover the oil. Wrap the dough in plastic wrap and place in the fridge for 1 to 2 hours to chill the coconut oil.
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4
Remove the dough from the fridge and roll it out into an 8 x 24-inch (20 x 61-cm) rectangle, fold the rectangle in thirds, then roll it out again into an 8 x 24-inch (20 x 61-cm) rectangle. Do this 5 times, letting the dough rest on the counter so the glutens in the flour relax if it gets too difficult to roll out. It's okay if the cold coconut oil pierces the dough in a few spots. Then wrap again in plastic wrap and refrigerate for 6 to 8 hours, or overnight.
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5
To make the filling, whisk the milk, sugar and cornstarch together in a small saucepan over medium-low heat. Continue to whisk until thick, 2 to 3 minutes. Then add the coconut oil, almond extract and vanilla extract, whisking until combined. Stir in the almond flour, transfer to a bowl and let cool in the fridge overnight along with the croissant dough.
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6
Have 2 half sheet pans lined with parchment nearby.
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7
Remove the dough and filling from the fridge. Unwrap the dough and roll it out on a lightly floured work surface, into a long 1/4-inch (6-mm)-thick rectangle, making sure the rectangle gets no wider than 9 inches (23 cm) across. If you need to cut the dough in half for it to fit on the work surface, that's fine, just keep the other half wrapped in the fridge while you work. Cut long triangles up the width of the rectangle that are about 5 inches (12.7 cm) across at the base. Roll 2 tablespoons (30 g) of the filling into a coil, and place it at the base of the triangle. Pull on the ends of the triangle gently to stretch them, then using your palm, press down and roll the triangle up onto itself. Place it on the baking sheet with the tip tucked under the bottom of the pastry. Cover it with plastic wrap, and continue until all the pastries are rolled. You should get about 14 croissants. Let them rise again for 1 to 2 hours, or until doubled in size.
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8
Preheat the oven to 425u00b0F (220u00b0C or gas mark 7) and place a rack in the lower upper part of the oven and another in the upper lower part of the oven.
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9
Uncover the croissants, sprinkle them with the sliced almonds and flaked coconut and bake for 20 to 22 minutes, or until puffed and browned on top and completely cooked though. Serve warm or at room temperature.
