• Preheat oven to 350°F. Line 2 baking sheets with parchment paper.

Prep The Peanut Butter Filling:

• In a small bowl, stir together the peanut butter and powdered sugar until fully combined and smooth. The mixture should be thick but scoopable. If it's very soft, cover and refrigerate for 10-15 minutes to firm slightly.
  

Make The Cookie Dough:

• In a large mixing bowl or the bowl of a stand mixer with the paddle attachment, beat the butter, brown sugar, and granulated sugar on medium speed until light and creamy, about 3-5 minutes.
• Add the egg yolk and vanilla, and beat until well combined, scraping down the sides of the bowl as needed.
• In a separate bowl, whisk together the flour, cocoa powder, and salt.
• With the mixer on low speed, gradually add the dry ingredients to the butter-sugar mixture and mix just until a thick, uniform dough forms and no dry flour is visible.

Shape And Bake The Cookies:

• Using a medium cookie scoop (about 1 1/2 tablespoons), portion the dough into balls and place them on the prepared sheet, spacing them about 2 inches apart.
  
• Gently roll each portion between your palms to smooth, then use the bottom of a clean drinking glass or your palm to slightly flatten the tops.
• Using your thumb or the rounded back of a measuring spoon, press a small, deep indentation in the center of each cookie, without pressing all the way through.
• Scoop about 1 teaspoon of the peanut butter filling, roll it into a ball, and nestle it into the indentation, pressing gently so it sits snugly in the center. Repeat with the remaining cookies and filling.
  
• Bake one sheet at a time for 12-15 minutes, or until the edges look set and the tops are slightly dry and no longer glossy.
• Let the cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool until just warm or at room temperature, about 30-45 minutes.

Finish And Serve the Cookies:

• While the cookies cool, place the chopped baking chocolate in a microwave-safe bowl. Microwave at 50% power for 30 seconds, then stir. Continue microwaving in 15‑ to 30‑second bursts at 50% power, stirring after each, until the chocolate is just melted and smooth.
• Using a spoon or piping bag, drizzle the melted chocolate over the cookies. Let the chocolate set at room temperature (about 30-45 minutes), or refrigerate them for 10-15 minutes to set faster.
• Serve once the chocolate has set, or store in an airtight container.