Prep the Chicken: Slice each chicken breast in half lengthwise, then pound them thin. Season both sides generously with salt and pepper.
Dredge & Sear: Dip each piece into the beaten eggs, shaking off excess. Coat thoroughly in panko breadcrumbs, pressing lightly to adhere. Let the breaded chicken rest while heating your pan.
Add a generous layer of avocado oil to a large skillet over medium-high heat. Once hot, sear the chicken until deeply golden and cooked through, flipping once. Remove from the pan and set aside.
Make the Piccata Sauce: In the same pan, sauté the shallot and garlic until softened and fragrant.
Pour in the white wine, scraping up the browned bits from the bottom of the pan. Let it reduce slightly.
Stir in the capers and lemon juice. Reduce heat to low and whisk in the butter, one piece at a time, until the sauce is glossy and emulsified.
Finish & Serve: Return the crispy chicken to the pan and spoon the sauce over the top. Let simmer gently for 1–2 minutes.
Serve immediately over angel hair pasta.