Grate the zucchini using a box grater, then squeeze out excess moisture with a clean towel or paper towel to prevent sogginess.
Heat olive oil in a skillet over medium heat until shimmering and fragrant.
Add the grated zucchini and cook, stirring occasionally, until it starts to soften and turn golden around the edges, about 3-4 minutes.
Stir in the corn kernels and cook for another 2-3 minutes, allowing the corn to heat through and soften slightly.
Reduce the heat to low and sprinkle the grated Parmesan evenly over the vegetables, letting it melt and create a cheesy crust while stirring gently to incorporate.
Continue cooking until the cheese is bubbly and slightly browned on top, about 2 minutes.
Season the hash with flaky sea salt and freshly ground black pepper to taste.
Remove from heat and let sit for a minute to settle before serving.
Serve warm, garnished with additional Parmesan or fresh herbs if desired.
