Position a rack in the center of the oven and heat the oven to 350°F. Spray a mini muffin tin with spray with cooking spray.
In a medium bowl, whisk the flour, salt, baking powder, and baking soda.
In a stand mixer fitted with the paddle attachment, beat the butter, sugar, and cocoa powder on medium speed until well blended, about 2 minutes. Scrape down the bowl and the beater. Add the eggs one at a time, mixing until blended after each addition, about 30 seconds, and adding the vanilla and peppermint extract along with the last egg. Continue mixing on medium speed until well blended, about 1 minute.
Add the cooled, melted chocolate and mix until just blended, about 30 seconds. Add the flour mixture and mix on low speed until well blended, about 1 minute.
Using a mini ice cream scoop or spoon, drop a tablespoon of dough into each cup of prepared mini muffin tins. Fill the muffin cups only about ⅔ full. Bake, one tin at a time, until the cookies are puffed and the tops are cracked and look dry, 11 to 15 minutes.
When the cookies are just out of the oven, use the end of a thick-handled wooden spoon to make a small, deep well in the center of each cookie.
Let the cookies sit on the muffin tin for 5 minutes and then transfer them to a rack to cool completely. (At this point, you can fill the cookies immediately, or store in an airtight container at room temperature for up to 3 days, or freeze for up to 1 month before filling.)
Make the filling
Melt the chocolate and butter in the microwave or in a medium bowl set in a skillet of barely simmering water, stirring with a rubber spatula until smooth.
Remove from the heat and set aside until cool and slightly thickened.
Fill the cookies
Spoon the chocolate mixture into the wells of the cooled cookies. Set aside until the chocolate firms up, about 1 hour.
Serve immediately or store in an airtight container at room temperature for up to 3 days.
