GRATE zucchini on coarse side of box grater. PLACE in colander; SPRINKLE with 1/2 tsp salt. LET stand for 30 minutes. Using clean towel, SQUEEZE out and DISCARD liquid.
STIR together zucchini, 1 slightly beaten egg, 2 Tbsp. chives, flour, parsley, mustard, garlic, remaining 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 in 400°F oven for about 7 minutes or until browned around edges. TURN over; COOK for about 5 minutes or until golden and crisp.
Meanwhile, in saucepan SET over medium heat, POUR in enough water to come 3 inches up the side; ADD vinegar and BRING to simmer over medium-high heat.
CRACK eggs into small dish; SLIDE one at a time into simmering water. COOK for 3 to 4 minutes or until desired doneness. REMOVE with slotted spoon; BLOT on paper towels.
TOP zucchini fritters with poached eggs; GARNISH with remaining chives.
Top with a tsp. of plain Greek yogurt, sour cream or crème fraîche if desired.
This recipe is an excellent source of protein and choline, and a good source of vitamin and folate.