In a large mixing bowl combine previously steamed and finely chopped broccoli, shredded carrots, parmesan cheese, green onions, garlic, egg, and flour; mix and stir until everything is thoroughly incorporated.
Heat peanut oil in a large nonstick skillet over medium-high heat.
Add 1/4 cup broccoli mixture into a measuring cup; pack it tight.
Drop the mixture into the hot oil and flatten it slightly.
Cook for 2 minutes; flip and continue to cook for 1 to 2 minutes more, or until golden brown. If it starts to burn, lower the heat to medium.
Repeat with the rest of the mixture. You may have to cook them in batches.
Remove the fritters from the skillet and transfer to a paper towel lined plate.
Serve with a side of plain yogurt.