Sift together the flour, baking powder, cocoa powder, and salt into a large bowl to remove lumps and aerate the dry ingredients—this creates a lighter, more tender cookie. Stir in both the white sugar and packed brown sugar until evenly distributed. In a separate bowl, whisk together the room-temperature eggs, vegetable oil, and vanilla extract until well combined. Pour the wet mixture into the dry ingredients and mix until just smooth, being careful not to overmix. The dough will be thick and fudgy. Cover and refrigerate for 15 minutes to allow the dough to firm up, which makes it easier to shape into balls.
Once the dough has chilled, scoop and roll it into 24 equal balls about the size of walnuts—I like to use a cookie scoop for consistency, which ensures even baking. Pour the 1 cup of powdered sugar into a shallow bowl and roll each ball generously in the sugar until completely coated. This creates the signature crinkled appearance as the cookies bake and crack. Arrange the coated balls on a parchment-lined baking sheet, spacing them about 2 inches apart to allow for spreading.
Bake at 350°F for 10-12 minutes until the cookies are set but still slightly soft in the center—they'll continue to set as they cool. The tops should appear cracked and the edges firm. Remove from the oven and let the cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely. I find that slightly underbaking them keeps the interior fudgy and tender, which pairs beautifully with the frosting.
Using an electric mixer, whip the softened cream cheese for about 1-2 minutes until creamy and smooth, scraping down the sides as needed. In a small bowl, sift the 2 cups of powdered sugar to remove any lumps—this prevents grittiness in the frosting. Gradually add the sifted powdered sugar to the cream cheese while mixing on medium speed. Pour in the heavy whipping cream and continue whipping on medium-high speed for 2-3 minutes until the frosting is light, fluffy, and spreadable. Stop occasionally to scrape the bowl and ensure even mixing.
Pair up the cooled cookies by size, selecting similar-sized cookies for each sandwich. Spoon or pipe a generous dollop of the frosting from Step 4 onto the flat side of one cookie, then gently press another cookie flat-side down on top to create a sandwich. Place the assembled cookies on a parchment-lined tray and refrigerate for 15 minutes to set the frosting and make them easier to handle. This also firms up the frosting slightly, making for a more pleasant texture contrast with the soft cookie.