In a medium skillet heat oil over medium heat. Add shallot and sweat, without obtaining any color, until soft, about 3-4 minutes. Add corn, season with sea salt, fresh ground pepper & herbs d'Provence, and sautée for approximately 5 minutes. Transfer mixture to a bowl and set aside.
Wipe out the skillet and set aside to use for the eggs.
In a medium bowl, whisk the eggs and milk until combined. Heat the skillet over medium-low heat. Add just enough butter to coat the bottom of the pan. Once the butter is melted and foamy add the eggs.
When the eggs begin to set (and not before), use a spatula or wooden spoon, and move the eggs inward towards the center of the pan. Continue around the pan in the same manner.
As curds start to form, add the corn mixture and gouda to the eggs and mix to combine. Continue moving the eggs around the pan until they are fully set.
Fold in the fresh basil.
Remove the pan from the heat, and transfer the eggs to your plate. Season with salt and pepper.