Place a chicken breast flat on a cutting board. With your non-dominant hand flat on top to hold it steady, position your knife at the thickest side of the breast, parallel to the cutting board. Slice horizontally through the center using long, smooth strokes to create two thinner cutlets. Repeat for all the chicken.
Dredge the cutlets immediately before cooking — if you wait too long, the chicken will get soggy. Pat the cutlets dry. In a bowl, combine the rice flour, cornstarch, salt, and white pepper. Coat all sides of the cutlets in the flour mixture by turning them over in the bowl until completely covered.
Drizzle avocado oil into a large skillet over medium-high heat. Once the oil has heated for about 30 seconds, add the chicken to the skillet. Cook for 4–5 minutes per side until the chicken is cooked through and has a golden crust. Transfer the chicken to a plate.
Reduce the heat to medium. Add the chicken broth, white wine vinegar, pressed garlic, lemon juice, capers, and butter. Simmer for 1–2 minutes. Add the chicken back into the sauce and cook for another 2–3 minutes.
Serve over rice, pasta, or mashed cauliflower. Enjoy!