1. Slice each shrimp along the back to open (butterfly) slightly. Whisk together eggs and cheese in a shallow dish; place flour in another shallow dish. Dredge shrimp lightly in flour, then coat completely in egg mixture.

2. Whisk together broth, wine, and lemon juice; set aside. Heat a large skillet over medium-high heat. Swirl in oil, then butter. Cook shrimp in 2 single-layer batches, adding more oil between batches as needed, until golden, about 1 1/2 minutes on each side; transfer each batch to a plate when done. Pour broth mixture into skillet and cook, swirling skillet, until reduced by half, 1 to 2 minutes. Remove from heat, add lemon slices and parsley, and pour over shrimp. Serve immediately.