Preheat the oven to 350 degrees F. Line 2 large, rimmed baking sheets with parchment paper.
In a large mixing bowl, combine the peanut butter with the sugar and coconut oil. Use an electric mixer or a large spoon to mix until well combined. Add the eggs, baking soda and vanilla, and mix well. Add the oats and mix until evenly incorporated.
Drop 2 tablespoons of dough per cookie onto the prepared baking sheets. These cookies spread while baking, so leave a couple of inches around each one. Gently shape them into a more rounded mound and press down lightly so they’re no taller than 1 inch.
Bake 8 to 10 minutes, until they’re just starting to turn golden around the edges. Be careful not to overbake. Let the cookies cool for 10 minutes before transferring them to a cooling rack. In the meantime, bake your next round of cookies.
Optional: Sprinkle the cookies lightly with flaky sea salt.