REMOVE leaves from chard; chop coarsely and set aside. Cut stems into 1/2-inch slices; set aside in separate bowl.
HEAT 1 tablespoon of the oil in large skillet over medium-high heat for several minutes. Add onion; cook 3 to 4 minutes, stirring frequently. Reduce heat to medium; add mushrooms, chard stems and garlic. Cook 3 to 4 minutes, stirring frequently. Remove mixture from skillet.
ADD remaining oil and squash to same skillet; cook 12 to 15 minutes or until tender, stirring frequently. Stir in mushroom mixture, leaves, vinegar and salt; cook and stir 3 to 4 minutes or until leaves begin to wilt. Make indentations for eggs; add eggs. Cover; cook 8 to 10 minutes or until eggs are set. Sprinkle with black pepper.
MAKE IT VEGAN
Boost the flavor and sprinkle the finished dish with fresh chopped chives or sage.