Preheat oven to 375 degrees F and line a baking sheet with parchment paper. Set it aside.
In a large mixing bowl, cream together the butter and sugars until light and fluffy, on high speed. About 2 minutes. Don't forget to scrape down the sides of the bowl a few times.
Add in the eggs, one at a time, beating well after each addition. Mix in the vanilla extract.
Add in the flour, baking soda, and salt. Mix until combined.
Portion the dough out by the rounded tablespoons and press a milk dud into the center of each, rolling them into a closed ball around the dud and then spacing out about 8 per baking sheet.
Top with a sprinkling of flaky sea salt, if desired. Bake for about 10 minutes, until the tops have just barely browned.
Let cool for 5 minutes on the baking sheet before transferring to a wire cooling rack to finish cooling.
Notes
Dough Consistency: If your dough is too soft for wrapping around the Milk Duds, it may be due to warm dough or overly soft butter. Chill the dough for 1-2 hours before scooping.Cooling After Baking: Let the baked cookies cool on the baking sheet for a few minutes to prevent the melted Milk Duds from sticking to the pan and keep the cookies intact.Reheating: To enjoy freshly baked cookies with a soft, melty texture, reheat them in the microwave for about 15 seconds.Storage: These cookies are best within 3-5 days. Store them in an airtight container at room temperature for freshness.Freezing: Freeze the cookies once they've cooled. Flash freeze them on a cookie sheet for an hour, then transfer to a freezer-safe container. They can be stored for up to 2 months. Thaw and enjoy when ready.