Grate carrot, zucchini, and yellow squash into ribbons with a cheese grater. Set into mixing bowl.
Add all ingredients, except for the olive oil, to the bowl and mix thoroughly until well incorporated.
Form the mixture into small patties (using about 2 tablespoons of batter for each).
Add 1 ½ of olive oil to a preheated medium sized skillet.
Place 3-4 patties into oil, cook for 1 ½ -2 minutes on each side until done. Set onto a plate and cover with foil to keep warm.
Prepare the rest of the patties until all of the mixture is gone, replenishing the oil as needed.