Cook all of the vegatables in the oil and butter under soft, about 10 minutes. Add seasonings. In a mixing bowl add eggs and cream and beat together under well blended. Add cheese to egg mixture and mix well. Add egg mixture to vegatables in frying pan and cook, moving the uncooked egg mixture to the bottom of the pan, about 10 minutes.
Preheat oven to 375. When eggs are mostly cooked, sprinkle feta cheese on top of fritatta and place in preheated oven for 10 to 12 minutes until eggs are cooked through and middle of dish is set. Remove from oven and let sit for a minute or two before slicing. Slice in 6 pieces. Serves six.