Preheat the oven to 350°F. Lightly grease a 10- to 12-ounce oven-safe ramekin.
In a medium bowl, whisk together the melted butter, brown sugar, and granulated sugar until smooth.
Add the egg yolk and vanilla extract. Whisk until fully combined and slightly glossy.
Stir in the flour, baking soda, and salt until a thick cookie dough forms. If the dough seems too dry or crumbly, mix in 1 teaspoon of milk.
Fold in the chocolate chips, reserving a few to sprinkle over the top.
Press the cookie dough evenly into the prepared ramekin and top with the remaining chocolate chips.
Bake for 16–20 minutes, or until the edges are lightly golden and the center is just set. Be careful not to overbake—the cookie will continue to set as it cools.
Let cool for 5–10 minutes, then sprinkle with flaky sea salt if desired. Enjoy warm on its own or with a scoop of vanilla ice cream.