Position racks in the lower and upper thirds of the oven and heat the oven to 350 degrees. Line two large sheet pans with parchment paper.
In the bowl of a stand mixer fitted with the whisk (or in a large bowl using a hand mixer), beat the peanut butter and sugar on high just until combined, about 1 minute. Add the eggs and salt and beat on medium until well combined, about 1 minute. Transfer half the dough to a bowl or a clean work surface.
Add the chocolate and cocoa powder to the remaining dough in the mixer bowl and beat on medium until combined.
Portion the peanut butter dough into 1-tablespoon spoons and the chocolate dough into heaping 1-tablespoon scoops. Squeeze together one scoop of peanut butter dough and one scoop of chocolate dough and roll into a neat ball. Transfer the balls to the prepared pans, at least 1½ inches apart. Using the flat bottom of a glass dipped in granulated sugar, press each ball into a flat round that is ½ inch thick. (After pressing the first cookie, the glass will be greasy enough for the sugar to adhere to it.)
Bake the cookies until set and slightly puffed, 14 to 16 minutes, switching racks and rotating the pans front to back halfway through. Transfer the baking sheets to wire racks to cool. (The cookies will be quite crumbly and delicate right after baking and need a few minutes to firm up.)
