Step 1: Prepare the Shrimp

1. Rinse the shrimp under cold water and pat them dry with paper towels. Season the shrimp with salt and pepper.
2. In a shallow bowl, place the flour. In a separate bowl, whisk together the eggs and water to create the egg wash.

Step 2: Coat and Fry the Shrimp

1. Heat 2 tablespoons of olive oil and 1 tablespoon of butter in a large skillet over medium heat.
2. Dredge each shrimp in the flour, shaking off any excess, then dip it into the egg wash to coat.
3. Place the shrimp in the skillet, working in batches to avoid overcrowding. Cook for 2-3 minutes on each side until golden brown and crispy. Transfer the cooked shrimp to a plate lined with paper towels and keep warm.

Step 3: Make the Sauce

1. In the same skillet, add the remaining tablespoon of butter and the minced garlic. Sauté for 1-2 minutes until fragrant.
2. Deglaze the pan with the white wine, scraping up any browned bits from the bottom. Let the wine simmer for 1-2 minutes to reduce slightly.
3. Add the chicken broth, lemon juice, and lemon zest. Stir in the capers, if using. Bring the sauce to a simmer and cook for 4-5 minutes, allowing the flavors to meld.

Step 4: Combine and Serve

1. Return the cooked shrimp to the skillet, spooning the sauce over the top. Let the shrimp simmer in the sauce for 1-2 minutes to absorb the flavors.
2. Garnish with fresh parsley and lemon slices.
3. Serve immediately over pasta, rice, or with crusty bread to soak up the sauce.