Heat oil in a large deep cast iron pan so it is about 1/2 inch deep to 350 degrees. (I store a large mason jar of coconut oil for frying in my fridge and sift the used oil back into the jar when I am finished frying).
In a small bowl mix the goat cheese and chopped basil.
Clean the zucchini blossoms and fill with about 1/2 tablespoon basil goat cheese (or cream cheese). Set aside.
Separate the eggs and whip the whites until soft peaks form. Slowly add in the yolks.
Dip the stuffed zucchini blossoms into the whipped egg mixture so it is covered on all sides.
Carefully place into the hot oil (working in batches if needed). Fry on all sides until golden brown, about 1 minute per side.
Remove from oil onto a paper towel to drain. Sprinkle with fine grain sea salt.