Step 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.
Step 2
Preheat the oven to 450 degrees F (230 degrees C). Line a baking sheet with a silicone mat.
Step 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.
Step 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.
Step 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.
Step 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.
Step 7
Melt chocolate in a microwave-safe glass or ceramic bowl in 15-second intervals stirring after each interval 1 to 3 minutes.
Step 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.