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For the puff pastry brioche dough
Make a puff pastry brioche dough following the directions on this
page.
For the pistachio cream
In an electric stand mixer, whisk together the ground pistachios,
brown sugar, and butter for at least 10 minutes. Add the eggs and
whip for 2 to 3 minutes. Transfer to a pastry bag.
For assembly and baking
Preheat the oven to 330°F (165°C). Roll out the dough to a thickness
of ⅛ inch (3 mm). Place a 9½-inch (24-cm)-diameter cake ring on
top of the dough and, using a knife, cut around the edge.
Repeat with an 8½-inch (22-cm)-diameter cake ring. Pipe the
pistachio cream in the center of this second circle, so that it does not
touch the edges.
Then place the first, larger circle on top. Press the two pieces
together to seal the edges. Finally, place a 7¼-inch (18-cm)-diameter
cake ring over the galette to serve as a guide. Using a knife, trim the
edges.
On a Silpat, ® spread out the softened butter, then cover with the
brown sugar and the rest of the pistachios and place the galette on
top. Place a 7½-inch (19-cm)-diameter cake ring around the galette.
Bake in the oven for about 45 minutes, then remove and turn over
the galette.