1) Remove the ends of the courgettes and, if they are large, cut in half lengthwise. Slice the courgettes diagonally in 1 1/4 cm slices. Heat 2 tablespoons of olive oil in a large saute pan and add the onions. Cook for 10 minutes on medium-low heat, until they start to brown. Add half the courgettes, 1 teaspoon salt, and 1/4 teaspoon pepper to the pan and cook, tossing occasionally, for 10 to 15 minutes, until just cooked through. Sprinkle with parmesan and cook for 30 seconds more. Remove to a serving platter and repeat with the rest of the courgettes. Serve immediately.
Note: If you cook too much courgette in one pan, you end up steaming rather than sauteing it. I prefer to cook it in 2 batches.