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1
In a large bowl, sift together the flour, salt, fleur de sel, white pepper, and cocoa powder. Set aside.
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2
In the bowl of a standing mixer fitted with the paddle attachment, beat the butter and sugars together until light and fluffy, about 3 minutes. Scrape down the bowl, and add the egg yolks, one at a time, beating until each is incorporated. Add the vanilla and melted chocolate and beat until uniform in color. Scrape down the sides and bottom of the bowl and beat again for 10 seconds.
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3
Add half of the dry ingredients and beat for 15 seconds. Again, scrape down the bowl, add the remaining dry ingredients and beat until just incorporated. Loosely shape the dough into two balls, wrap them tightly in plastic wrap, and refrigerate them for at least 3 hours.
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4
Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper.
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5
Unwrap one ball of dough and divide it into two equal portions. Place the first portion on a lightly flour-dusted work surface and return the other to the refrigerator.
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6
Use your hands to knead the dough until pliable and form into a small disc. Roll the dough into a 1/4 -inch-thick round. It will be slightly sticky, so you may have to flip and lightly flour it a few times while you work. Use a 2-inch round cookie cutter to create your sandwich tops and bottoms, and transfer them to the prepared baking sheets, leaving about 1 inch of space around each cookie. Continue the process with the remaining dough. Extra dough scraps can be refrigerated and rerolled, if desired.
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7
Sprinkle the tops of the cookies with a little fleur de sel, then bake them for 10 to 12 minutes, rotating the sheets halfway through the baking time. The tops of the cookies should look a bit dry and possibly cracked. Place the baking sheets on wire racks to cool for 5 minutes. Use a spatula to transfer the cookies to the racks to cool completely before filling them.
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8
In the bowl of a standing mixer fitted with the paddle attachment, beat the shortening and butter until lump free and smooth. Add the sugar in three parts, mixing each part until just combined. Add the salt, vanilla, and rum and beat again for 10 seconds. The filling should be thick but spreadable (like the inside of an Oreo). If it is too thick, add a drop or two of water as needed. Keep adding water to reach the desired consistency, but do not add too much water or the filling will be too thin.
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9
Alternatively if the mixture is too thin, add a few tablespoons of confectioners' sugar.
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10
Use a pastry bag or a small spoon to apply about 2 tablespoons of filling to the flat side of a cookie. Place another cookie, flat side down, on top. Press down slightly so that the filling spreads to the edges of the cookie. Repeat until all the sandwich cookies are made. Let them set up for about 15 minutes before serving. Store the cookies at room temperature in an airtight container for up to 3 days.
