In a medium-sized bowl, whisk together the flour, cocoa powder, salt, and baking soda. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, cream together the butter, 2/3 cup (133 grams) granulated sugar, and light brown sugar on medium speed until well combined, about 1 minute. Scrape the sides of the bowl and add the egg and vanilla extract, stirring on medium speed just until combined. Add the mixed bowl of dry ingredients and stir on low speed, scraping the bowl as needed, just until the dough comes together. Fold in any unincorporated flour and set aside.
Line 2 heavy-bottomed baking sheets with a piece of parchment paper and pour the remaining 1/3 cup (67 grams) granulated sugar in a small mixing bowl. Use a small (2-teaspoon) spring-loaded scoop with portion out rounds of dough. Briefly roll each piece in your hands to smooth and toss each one in the remaining sugar to coat. Use your thumb or the back of a rounded ½ teaspoon measure to indent a thumbprint into each cookie. Space them 2” apart on the prepared pans and cover each with plastic wrap, refrigerating until firm, about 30 minutes.
About 15 minutes prior to baking, preheat the oven to 350 °F (180 °C). Bake the cookies one at a time in the preheated oven just until the edges of the cookies are set, about 10 minutes. The centers of the cookies will likely have puffed some while baking, so immediately after removing the pans from the oven, use the back of the ½ teaspoon measure to re-create a thumbprint in the center of the cookie again. Allow the cookies to cool completely.
Fill a piping bag fitted with a round tip with the peanut butter cup filling. Pipe teaspoon-sized swirls of filling into the center of each cooled cookie. Sprinkle cookies with finely chopped honey roasted peanuts if desired. Allow to set up slightly prior to enjoying. Cookies can be stored at room temperature in an airtight container and are best eaten within 3 days.
To make the filling:
In a medium-sized mixing bowl, use a hand mixer to combine the peanut butter, confectioner’s sugar, and milk on low speed. Stir until smooth.