Beat melted butter, granulated sugar, and brown sugar for 2 minutes. Mix in egg and 2 tsp vanilla. In a separate bowl, whisk flour, cocoa, baking soda, and salt. Stir dry ingredients into the wet mixture until a thick dough forms.

Preheat oven to 350°F (175°C). Scoop dough into 1-tablespoon balls, place on lined baking sheets, and press a deep indent into the center of each. Bake for 8 to 10 minutes, then re-press the indent immediately after removing from the oven.

While cookies cool slightly, beat peanut butter, 3 tbsp softened butter, powdered sugar, and 1/2 tsp vanilla until smooth and pliable, about 1 minute.

While cookies are warm, spoon about a teaspoon of the peanut butter mixture into each indent, pressing gently to fill. Let cool on the sheet for 10 minutes, then transfer to a rack to cool completely.

Melt chocolate and coconut oil in 15-second bursts, stirring until smooth. Drizzle over the cooled cookies and let set at room temperature, about 15 minutes.