To Prepare the Cookies:

Combine dry ingredients:

1. In a medium bowl, sift together the flour, baking soda, and salt. Stir in the chopped milk chocolate; set aside.

Cream the butter and sugars:

1. In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, granulated sugar, and brown sugar until light and fluffy, scraping down the sides of the bowl as needed.

Add eggs, vanilla, and peanut butter:

1. Add the eggs one at a time, ensuring each is fully incorporated before adding the next. Stir in the vanilla extract and peanut butter, mixing just until blended.

Incorporate the dry mixture:

1. Add half of the flour mixture and mix for approximately 15 seconds. Add the remaining flour mixture and continue mixing until just combined. Do not overmix.

Chill the dough:

1. Cover the bowl with plastic wrap and refrigerate the dough for a minimum of 3 hours to ensure proper texture and prevent spreading during baking.

Preheat the oven:

1. Set the oven to 375°F (190°C) and line baking sheets with parchment paper.

Shape and bake:

1. Drop the chilled dough by rounded teaspoons onto the prepared baking sheets, spacing each approximately 2 inches apart. Gently press each ball to form a thick disc, being careful not to flatten completely. Sprinkle lightly with granulated sugar.

Bake the cookies:

1. Bake for 8 minutes, or until the tops of the cookies begin to brown slightly. Remove the baking sheet from the oven and allow cookies to rest for 2 minutes. Transfer cookies to a wire rack to cool completely.

To Prepare the Filling:

Create the ganache:

1. Place the chopped milk chocolate, peanut butter, powdered sugar, and salt in a medium heat-safe bowl.

Heat the cream:

1. In a small saucepan over medium heat, bring the whipping cream just to a boil. Immediately pour the hot cream over the chocolate mixture.

Stir until smooth:

1. Allow the mixture to sit for a minute, then stir until the chocolate is fully melted and the filling is smooth and glossy. Transfer to the refrigerator and chill until thick and spreadable, approximately 1 hour.

To Assemble the Sandwich Cookies:

1. Once the cookies are fully cooled and the filling has set, spread approximately 1 rounded teaspoon of filling onto the flat side of one cookie.
2. Top with a second cookie, pressing gently to form a sandwich.
3. Repeat the process with the remaining cookies and filling.
4. Store the assembled cookies in an airtight container at room temperature.