In a stand mixer or with a hand mixer, cream the sugar and softened butter together until fluffy and the sugar has dissolved. This will take 2-3 minutes in a stand mixer on medium low speed.  Mix in the vanilla. With the mixer on low, slowly add the flour. Stop the mixer once a crumbly dough forms. 

Dump out the dough onto a piece of parchment or plastic wrap. Using your hands, shape it into a log that is about 6 inches long and about 2 inches in diameter. Wrap the log, then place it in the fridge to chill for at least one hour. You can easily do this part a day ahead of time if you like. 

Pre-heat your oven to 350 degrees and line a standard baking sheet with parchment or a silicone baking mat. Remove the dough from the fridge and unwrap it. Using a very sharp knife, carefully slice the dough log into rounds that are roughly 1/4-inch thick in diameter. Place the slices of dough onto the prepared baking sheet. Sprinkle the tops with a bit of coarse sea salt. Bake for 10-12 minutes or until the bottom edges are just beginning to get a hint of color. Cool at least 15 minutes on the baking sheet before moving the cookies to a rack to cool completely.