Cut each zucchini lengthwise into thin even 1/4-inch thick slices. (This is most easily done on a mandolin.) You will need 16 slices total. Lay them out in pairs on paper towels or a clean tea towel and season lightly with salt and pepper.
Arrange the prosciutto slices on half the zucchini slices so none hangs over the edges. Place 2 sage leaves on top. Place the cheese slices on top, taking the same precautions you did with the prosciutto. Finally, lay the remaining zucchini slices on top of each stack. Cover with paper towels or another clean tea towel, and press down firmly to extract moisture and firm the zucchini.
Pour the eggs into a deep plate. Season the flour with salt and pepper and put it on another plate. Pick up each zucchini stack by both ends and hold it securely closed as you dip it first in the egg and then dredge in the flour until evenly coated.
In a skillet large enough to hold at least 3 zucchini stacks at a time, heat the olive oil over medium-high heat until hot. Cook the zucchini, turning once, until golden brown, about 2 minutes on each side. Remove to a plate and keep warm until all are cooked. Add more oil by tablespoonfuls, if needed.
Add the remaining sage leaves to the hot pan and cook briefly until crisp. Arrange several crisped leaves on top of each saltimbocca. Serve with a sprinkling of parsley, a light dusting of Parmesan, and lemon wedges.