Pulse the oatmeal in a food processor fitted with a metal blade until some of it is fine and some of it is still very coarse. Whisk the processed oatmeal with the flours, baking powder, baking soda and salt.
Cream the butter and the sugars in a mixer fitted with a paddle attachment until they are very light, about 5 minutes. Beat in the egg one at a time, mixing well. Beat in the vanilla. Reduce the speed to low and add the flour mixture until combined. Fold in the chocolate chips. Wrap the dough with plastic and refrigerate for at least 24 hours and up to 48 hours.
Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper. Scoop the dough 1 teaspoonful at a time into balls and place onto the baking sheet leaving 1 inch between each one. Sprinkle lightly with sea salt. Bake until golden brown around the edges and paler and soft in the middle, 10 to 12 minutes. (If baking two sheets at a time, rotate the sheets halfway through the baking time, swiveling them back to front, and top to bottom.) Cool 10 minutes on the sheet on a rack, then transfer cookies to a rack and cool as long as you can resist.
Cook's Note: You can make these twice as large if you'd like, just increase the cooking time by about 2 minutes.