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Whisk together the flour, baking powder, and salt; set aside. In the bowl of a stand mixer, using the paddle attachment, cream together the butter and sugar at medium-high speed until fluffy, about 2 minutes, scraping the bowl as necessary. Add the flax seed egg replacer and vanilla, and beat until combined.
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Gradually add the flour mixture to the butter and sugar mixture, mixing at low speed just until combined. Wrap the dough tightly in plastic wrap, and refrigerate while waiting for the dough to finish its rise.
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Lightly grease a large baking sheet, or line with parchment paper. Turn the dough out onto a lightly floured surface, and gently deflate. Divide the dough evenly into 8 pieces. Round each piece into a ball, and transfer to the prepared baking sheet.
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Cover the dough balls loosely with lightly-oiled plastic wrap, and let sit at room temperature while you get the cookie covers ready.
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Unwrap the cookie dough, and divide it into 8 even pieces. Roll each into a ball, keeping unused pieces covered. Press each ball into a flat circle about, about 3 1/2 inches in diameter.
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Drape each piece of cookie dough over the bread dough, being careful not to deflate the rising dough. The cookie dough should encase the top and sides, but not the bottom, of each roll. With a sharp paring knife, score each round with a crosshatch pattern.
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Preheat the oven to 350*F. Let the dough balls rise for about an hour and then bake for 25 minutes, or until barely golden brown on top. Transfer to a wire rack to cool. Eat the same day for the best taste and mouthfeel.