For the cookies: Adjust the racks to the top and lower thirds of the oven and preheat to 375 degrees F. Line two baking sheets with parchment paper.
Whisk together the flour, baking powder and salt in a medium bowl and set aside.
Combine the butter and almond butter in the bowl of a stand mixer fitted with a paddle attachment (or in a large bowl if using a hand mixer). Beat on medium-high speed until smooth and combined. Scrape down the sides of the bowl.
Add the brown sugar and 1/3 cup of the granulated sugar and continue to beat until light and fluffy, about 3 minutes.
Add the egg and vanilla and beat until combined. Adjust the speed to medium-low and add the flour in two batches, mixing until just incorporated.
Combine the chopped almonds and the remaining 3 tablespoons granulated sugar in a small bowl.
Scoop out even tablespoons of cookie dough, roll into balls and then dredge in the almond-sugar mixture. Space the balls about 2 inches apart on the prepared baking sheets.
Bake until the cookies appear dry and slightly cracked on the top and golden brown on the bottom, 10 to 12 minutes.
Use the rounded side of a teaspoon to make an indentation in the center of each cookie.
Let them cool for a few minutes on the baking sheets, and then transfer to a rack to cool completely.
For the chocolate ganache filling: While the cookies cool, combine the chocolate and heavy cream in a microwave-safe bowl and heat for 45 second increments, stirring well between each, until smooth.
Let cool completely at room temperature.
Fill a pastry bag fitted with a medium star tip with the chocolate ganache. Pipe about 1 teaspoon of the ganache into the center of each cookie.
Serve, or refrigerate in an airtight container for up to 3 days.
