In a wide shallow bowl, beat eggs with garlic, parsley, and 1/2 teaspoon each salt and pepper. In a separate bowl, combine breadcrumbs and Parmesan. Dip each cutlet into egg mixture to coat completely, then dredge in breadcrumb mixture, patting it on with your fingers.
Heat 2 tablespoons oil in a large nonstick skillet over medium-high heat. Cook 2 cutlets until golden brown and cooked through, about 3 minutes per side. Transfer to a platter. Add remaining 2 tablespoons oil to pan, reduce heat to medium, and repeat with remaining 2 cutlets.
Wipe skillet with a paper towel; heat butter until melted. Add wine; heat 30 seconds. Stir in broth and lemon juice; simmer 2 minutes. Season with salt and pepper. To serve, pour broth mixture over cutlets.
For a side dish, toss cooked egg noodles with some butter, and sprinkle with fresh parsley. Serve with lemon wedges that can be squeezed over the chicken.