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1
Mix butter, brown sugar, flour, and salt together in a large bowl using a spatula. Place dough between two sheets of waxed paper or inside a zip-top bag. Press or roll dough to 1/4-inch thickness. Trim off the edges slightly to get a rectangular shape, if desired. Freeze crust until ready to use.
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2
Preheat the oven to 450 degrees F (230 degrees C). Line a baking sheet with a silicone mat.
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3
Combine water, butter, and salt in a saucepan; bring to a simmer over medium heat. Add flour; stir with a wooden spoon until mixture comes together into a smooth dough and pulls away cleanly from the bottom of the pan. Transfer to a bowl and spread out with a whisk to speed up cooling. Cool until warm, about 10 minutes.
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4
Whisk eggs, one at a time, into the pastry, mixing well after each addition. Finish mixing with a spatula. Scoop pastry into a pastry bag and pipe into 6 to 8 buns on the baking sheet. Smooth out tops with a wet finger.
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5
Use a cookie cutter to cut crust into circles about the diameter of the buns. Lightly push crusts onto the buns, just enough to secure them.
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6
Place buns in the preheated oven. Immediately reduce heat to 350 degrees F (175 degrees C) and bake until browned and fully puffed, 30 to 40 minutes. Transfer buns onto a cooling rack and place rack back on the baking sheet. Place in the turned-off oven, leave door partially open, and let cool completely, at least 20 minutes.
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7
Melt chocolate in a microwave-safe glass or ceramic bowl in 15-second intervals, stirring after each interval, 1 to 3 minutes.
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8
Spread a few teaspoons of melted chocolate onto the bottom of each bun. Gently press each chocolate base back on the baking sheet to spread it evenly. Let chocolate harden, about 1 hour.
