In a small bowl, beat together egg and vanilla extract until the yolk is broken up and evenly combined; set aside.
Combine flour, sugar, salt, and baking powder in the bowl of a food processor fitted with a blade attachment and pulse a few times to aerate and break up any lumps. Add butter and pulse until the mixture looks like sand, about 25 1-second pulses. Add egg mixture and pulse just until the dough forms into a ball, about 25 1-second pulses.
Turn dough out onto a clean work surface and roll into 2 logs, each about 1 1/2 inches in diameter. Wrap the logs in plastic wrap and refrigerate until just firm but still pliable, about 30 minutes. (The logs will flatten slightly while chilling. If you have a paper towel tube available, cut it in half lengthwise and nestle the cookie dough in there; this will help the dough keep its cylindrical shape while it chills.) Reshape the logs so they are perfectly round and refrigerate until firm, about 30 minutes more.
Heat the oven to 375°F and arrange a rack in the middle. Remove a dough log from the refrigerator, remove the plastic wrap, and slice the dough into 1/8-inch coins. Place the cookies 1/2 inch apart on an ungreased baking sheet. (About 30 cookies will fit on 1 sheet.) Rewrap the extra cookie dough in plastic and refrigerate until ready to bake the second batch. Bake the cookies until the edges are golden brown, about 8 to 10 minutes. Remove to a wire rack to cool completely. Repeat with the remaining dough.
Meanwhile, place peanut butter, powdered sugar, and vanilla in a small bowl and stir until smooth.
Using a butter knife, evenly spread 1/2 teaspoon of the peanut butter filling on each cooled cookie.
Line two baking sheets with parchment paper; set aside.
Prepare an ice water bath by filling a large bowl with 2 inches of cold water and adding 3 to 4 ice cubes; set aside.
Bring a medium saucepan filled with 1 to 2 inches of water to a simmer over high heat; once simmering, turn off heat. Place 18 ounces of the chocolate couverture in a dry, heatproof bowl. Set the bowl over the saucepan and stir until the chocolate is completely melted and has reached 118°F (Make sure the chocolate does not come in contact with water or exceed 120°F If either happens, start over, as the chocolate will no longer be usable.).
Remove the bowl from the saucepan. Add the remaining 6 ounces chocolate and stir until all the chocolate has melted and the temperature has cooled to 80°F To speed up the cooling process—but only after all of the chocolate has melted—place the bowl over the reserved ice water bath.
Once cooled, return the bowl of chocolate to the saucepan and stir until the chocolate reaches 86°F; immediately remove from heat. Do not remove the thermometer from the bowl; check the temperature periodically to make sure it stays between 85°F and 87°F (The chocolate must remain in this temperature range while dipping the cookies or it will not set properly.) Keep the saucepan of water over low heat and, when needed, set the bowl of chocolate over it to reheat.
To test if the chocolate is properly tempered, spread a thin layer on parchment paper and place it in the refrigerator for 3 minutes to set. If the chocolate hardens smooth and without streaks, it is properly tempered. (If it is not properly tempered, let the melted chocolate harden and start the tempering process over again: Bring the chocolate up to 118°F, then down to 80°F, then up again to 86°F.).
Using a dinner fork, dip the cooled cookies one at a time, peanut butter side up, into the chocolate until covered. Lift each cookie out of the chocolate and tap the fork several times on the edge of the bowl. Scrape the bottom of the fork against the edge of the bowl to remove any excess chocolate.
Place the cookies on the prepared baking sheets by tilting the fork so that the edge of each cookie touches the parchment-lined pan, then pull the fork out. Repeat until all the cookies have been dipped. Let sit at room temperature until completely set, about 20 minutes. Store in an airtight container at room temperature for 1 week or in the freezer for up to 1 month.