Shred or grate zucchini . Using fine sieve, press shredded zucchini against sieve to remove as much moisture as possible. Alternately, squeeze handfuls of shredded zucchini to remove as much moisture as possible.
In a glass mixing bowl, soften cream cheese for about 15 seconds in the microwave oven. Add the Parmesan cheese & stir. Add one egg, stir vigorously to combine & then add the second egg and stir again.
To the egg mixture add the zucchini, scallions, garlic, salt, pepper, basil & cayenne. Stir until well combined. The mixture will be a bit "loose" because of the egg, but will come together when cooked.
Heat a well seasoned cast iron skillet over medium heat. Add the olive oil & butter. Using an ice cream scoop, portion the fritter mixture into the skillet. My pan is large enough for four small fritters at a time. Cover the skillet with a lid and allow to cook for a few minutes, until the bottom is golden brown.
Gently flip & cover with lid again for a couple of minutes until cooked through. Serve with sour cream.