Preheat the oven to 350 degrees F. Spray baking sheets with nonstick spray (or line with parchment or silpat mats).
In a medium bowl, whisk together the flour, baking soda and salt. Set aside.
In a large bowl, use an electric mixer at medium speed to combine the butter, peanut butter and sugars. Beat in the eggs one at a time until they are incorporated. Add the dry ingredients and beat until combined.
Stir in the oats and the chocolate chips.
Drop the cookies in rounded tablespoonfuls onto the cookie sheet, 3 inches apart. Sprinkle lightly with sea salt. Bake 10 to 15 minutes, or until cookies are set and cooked through to the middle. Timing will probably be about 12 minutes, but check first batch at 10, and then keep checking at 1 minute intervals until they are looking perfect. Then you can set timing for the remaining batches.
Notes
*Substitute old-fashioned oats if you need to... they'll just give the cookie a bit more texture.