Prepare the ingredients: Grate root vegetables like carrots, parsnips, and sweet potato on the large holes of a box grater. Grate and drain zucchini and summer squash. Chop and steam cauliflower and broccoli florets. Cut corn off the cob.
Blanch leafy greens: If using leafy greens like Swiss chard, add the chopped greens and their chopped steams to salted boiling water for 30 seconds. Remove with a slotted spoon and plunge them into the ice bath to stop the cooking process. Once blanched, drain and chop the greens.
Whisk the egg: In a large bowl, whisk the egg thoroughly.
Add the vegetables: Squeeze handfuls of wet vegetables, like blanched leafy greens or grated zucchini, to remove excess liquid before adding them to the bowl
Add the remaining ingredients: Add the cheese, ¼ cup of flour, herbs, spices, garlic, salt, and pepper to the bowl.
Mix the batter: Use a spatula to mix everything together so that it's evenly combined.
Test the batter: Check to see if you can form a patty in your hands and it holds together. If not, add a little more flour to the mixture.
Heat the oil and add the batter: Heat the oil in a large skillet or frying pan, preferably cast iron or nonstick, over medium-high heat until shimmering. Drop ¼ cup of batter into the pan, flatten it slightly with a flat spatula, and continue dropping more batter, leaving about 2 inches of space between the fritters and being careful not to overcrowd the pan.
Fry the fritters: Let the fritters cook undisturbed until browned on the bottom, 2 to 3 minutes. Flip the patties with the spatula and cook until browned on the second side, 2 to 3 minutes more.
Drain the fritters: Remove the fritters to a paper towel-lined large plate. Repeat making the fritters.
Serve the fritters: Transfer the fritters to a plate and serve warm, at room temperature, or cold with a dipping sauce of your choice, if using.