Preheat the oven then preheat it to 360°F. Line cookie sheets with parchment paper or silicone baking mats. (Read notes)
In a large bowl, whisk together the melted butter, cream cheese, brown sugar, and granulated sugar until smooth, glossy, and fully combined.
½ cup butter, 2 oz full-fat brick cream cheese, ⅔ cup brown sugar, ½ cup granulated sugar
Whisk in the egg yolks, vanilla, and milk until the mixture is cohesive and shiny.
2 large egg yolks, 2 teaspoons vanilla extract, 1 tablespoon milk
Switch to a spatula. Add the flour, cornstarch, baking soda, and salt. Fold gently just until no dry flour remains. Do not overmix.
1¾ cups all-purpose flour, 1 teaspoon cornstarch, 1 teaspoon baking soda, ½ teaspoon salt
Stir in the chocolate chips or chunks. (You can reserve some to press on top after baking.)
1 & 1/2 cups chocolate chips or chunks
Scoop 3 tablespoons of dough per cookie. Place 4 cookies max per sheet, spaced well apart.
Bake one pan at a time for 10-11 minutes, until edges are set and lightly golden, centers still look slightly soft and puffy still.
Remove from the oven. Press extra chocolate on top if desired. (highly recommended)
Let cookies cool on the pan for 15 minutes before transferring carefully to a wire rack.