Grate zucchini on the coarse side of a box grater. This step is critical: place shredded zucchini in a clean dish towel and wring out as much liquid as possible. Really squeeze it. Wet zucchini = soggy fritters that won't brown.
In a bowl, combine squeezed zucchini, eggs, flour, grated parmesan, salt, and pepper. Mix until combined. The mixture should hold together when pressed.
Heat olive oil in a large skillet over medium-high heat until shimmering.
Drop ¼ cup portions of mixture into the pan, press flat with a spatula to about ½ inch thick.
Cook 3–4 minutes per side until deep golden brown. Resist the urge to flip early.
Drain on paper towels. Serve warm with Greek yogurt.