Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper to prevent sticking.
In a large mixing bowl, use an electric mixer to cream together the softened salted butter, granulated white sugar, and packed light brown sugar until the mixture is light and fluffy.
Add in the creamy peanut butter, large egg, and vanilla extract. Mix until well combined.
In a separate bowl, whisk together the all-purpose flour until it is aerated. Gradually add the flour to the peanut butter mixture, mixing until just combined.
Using a cookie scoop, portion out the dough and roll it into balls. Place the dough balls on the prepared baking sheet, leaving enough space between each one.
Using your thumb (or the back of a measuring spoon), gently press down in the center of each dough ball to create a small well for the chocolate ganache.
Bake in the preheated oven for about 10-12 minutes or until the edges are lightly golden. Remove from the oven and allow to cool on the baking sheet for a few minutes before transferring to a wire rack.
While the cookies are cooling, place the semi-sweet chocolate chips in a heatproof bowl. In a small saucepan or microwave, heat the heavy cream until it’s just about to simmer. Pour the hot cream over the chocolate chips and let sit for a minute before stirring until smooth.
Once the cookies are completely cooled, use a spoon or piping bag to fill each thumbprint with the warm chocolate ganache. Allow the ganache to set before serving.