Beat the brown sugar and butter with the paddle attachment of a stand mixer (or with a handheld mixer in a large bowl). Add eggs and vanilla and beat to combine.
Add the baking soda and fine-grain salt and beat to combine, then add the flour and stir just until combined. Stir in the chocolate chips.
Wrap the dough in foil or plastic wrap (or simply cover the bowl) and refrigerate for at least 2 hours and up to 3 days.
Heat the oven to 350°F and grease one or two baking sheets (or line them with parchment paper). Drop the dough by the rounded tablespoonful onto the baking sheet(s), leaving 2 inches between cookies. Sprinkle a small pinch of coarse sea salt on each cookie, then bake until the cookies are mostly firm and their edges are golden brown, 9 to 11 minutes.
Transfer the cookies to wire racks or paper towels, and repeat with the remaining dough and salt. Serve warm.
