How to Make It
In a stand mixer fitted with the paddle, combine 3 1/2 cups of the flour with 3 sticks of the cubed butter, the granulated sugar and 1 tablespoon of salt. Beat at low speed until some of the butter is the size of peas, about 3 minutes. With the machine on, beat in the water until a lumpy dough forms, about 2 minutes. Scrape the dough onto a lightly floured work surface and knead gently to form a ball. Pat the dough into a large rectangle, dust with flour and wrap in plastic. Refrigerate 1 hour or overnight.
Preheat the oven to 375°. In a large bowl, toss the blackberries with the confectioners’ sugar, lemon juice and zest. In another large bowl, using your hands, combine the oats with the brown sugar, coconut, flax seeds, cinnamon, 1 teaspoon of salt, the remaining 6 tablespoons of butter and the remaining 1/2 cup of flour; mix until crumbly.
On a lightly floured work surface, roll the dough out to a 15-inch round, about 1/2 inch thick. Transfer the dough to a 12-inch cast-iron skillet and pat into the bottom and up the side of the skillet, letting about 2 inches of dough drape over the side. Spread the oat crumble over the dough in the bottom of the skillet and top with the blackberries. Fold the overhanging dough over the blackberries. Brush the top of the dough with the beaten egg yolk and sprinkle with granulated sugar. Bake for about 45 minutes, until, then tent the crust with foil, leaving the blackberries exposed. Bake for an additional 20 minutes, until the bottom is crisp.
Meanwhile, in a medium bowl, using a wooden spoon, whip the mascarpone until light and fluffy. Serve the galette warm or at room temperature with the whipped mascarpone.