In a saucepan, melt the butter and chopped chocolate over medium low heat. Stir it frequently, and remove from the heat as soon as it's melted. Pour into a mixing bowl.
Add the granulated sugar, brown sugar, vanilla, egg and egg yolk. Whisk vigorously, as hard as you can, for 2 full minutes, until the mixture has lightened in color.
In a separate bowl, sift together the flour, cocoa powder, corn starch, baking soda and salt, and whisk until evenly distributed. Add the dry ingredients to the wet ingredients and use a spatula to fold everything together into a dough. Let the dough rest and cool for 10 minutes, then fold in the chocolate chips.
Use a medium cookie scoop to portion the dough into 20 portions (about 2 tablespoons each). Roll each portion of dough into a smooth ball with your hands, and ever so slightly flatten each ball. Cover the dough balls with plastic wrap to keep them moist while you preheat the oven.
Preheat the oven to 350 F, and position a rack in the center of the oven. Line a baking sheet with parchment paper.
Bake 6 cookies at a time, so they have room to spread out, baking them for exactly 8 minutes. (Let the remaining dough balls sit covered at room temperature.) Take the cookies out of the oven, and immediately use a round cookie cutter (one that's larger than the circumference of the baked cookies) and "scoot" it around the hot cookies to pull in the edges for perfectly round cookies. Cool the cookies on the baking sheet for 2 minutes, then transfer to a cooling rack to cool completely.
Bake the remainder of the dough, 6 cookies at a time, until you've baked all the cookies.