Preheat the oven to 375°F.
Line two large baking sheets with parchment paper. Place the turbinado sugar into a shallow bowl.
In the bowl of a stand mixer fitted with the paddle attachment (or using a hand mixer), beat together the butter, peanut butter, granulated sugar, and brown sugar on medium speed for 2–3 minutes until light and fluffy.
Scrape down the sides of the bowl as needed.
Mix in the eggs one at a time, beating well after each addition.
Add the vanilla extract and mix until fully incorporated.
Add the flour, cornstarch, baking soda, and kosher salt.
Mix on low speed just until the flour disappears. Avoid overmixing.
Using a large cookie scoop (about 3 tablespoons each), portion the dough.
Roll each dough ball in the turbinado sugar until completely coated.
Arrange on the prepared baking sheets, leaving about 2½ inches between each cookie. There is no need to flatten the dough.
Bake for 10–11 minutes, or until the edges are lightly golden while the centers still look slightly underbaked.
Immediately sprinkle the tops with flaky sea salt if desired.
Allow the cookies to cool on the baking sheet for 10 minutes before transferring to a wire rack to cool completely. The cookies must be completely cool before adding the chocolate.
Place the chopped chocolate or melting wafers into a microwave-safe bowl. Microwave in 30-second intervals at 50% power, stirring well between each, until completely smooth.
Allow the melted chocolate to cool for 5–10 minutes before using. This gives the chocolate time to thicken slightly, making it much easier to work with. Slightly cooled chocolate pipes more neatly and won't drizzle everywhere, creating a thicker, more even chocolate layer.
Choose one of these three methods:
Method 1 (My Favorite): Pipe right onto the cookie. Transfer the slightly cooled chocolate to a piping bag and snip a small opening. Pipe about 1 tablespoon of chocolate onto the center of the bottom of each cookie. Place the cookie chocolate-side down onto a silicone baking mat or parchment paper and gently press to spread the chocolate into an even layer.
Method 2: Pipe onto the parchment. Pipe a small circle of chocolate directly onto parchment paper or a silicone baking mat. Immediately press the cookie into the chocolate, gently twisting if needed to spread it evenly.Lift carefully if necessary and reposition.
Method 3: Dip the cookie. Dip the bottom of each cookie directly into the bowl of chocolate. Allow any excess chocolate to drip back into the bowl. Place chocolate side down onto parchment paper or a silicone baking mat.
Transfer the cookies to the refrigerator for 15–20 minutes, or until the chocolate is completely set.