Place zucchini in colander and sprinkle with 1/2 teaspoon salt.
Allow to stand for 30 minutes.
Using a tea towel, squeeze out and discard liquid.
In a mixing bowl, stir together zucchini, 1 beaten egg, 2 tablespoons of chives, flour, parsley, mustard, garlic, remaining 1/2 teaspoon of salt, and pepper.
Stir in parmesan cheese.
Line baking sheet with parchment paper and spray lightly with cooking spray.
Scoop 1/4 cup zucchini mixture and shape into thin patty; repeat with remaining zucchini mixture. Lay patties on parchment paper, 1-inch apart.
Bake for 7 minutes or until browned around edges. Turn over; cook for approx.
5 minutes (until golden & crisp).
In a saucepan set over medium heat, pour in enough water to come three inches up the side; add vinegar and bring to simmer. Crack eggs into a dish; slide one at a time into simmering water.
Cook approx. 3–4 minutes or until desired doneness. Remove with slotted spoon; blot on paper towels.
Top zucchini fritters with poached eggs; garnish with remaining chives.