Season chicken, on all sides, with salt and pepper. In a large bowl, dredge chicken in cornstarch until evenly coated. Using tongs, shake off excess cornstarch. In a separate large bowl, toss chicken in eggs until evenly coated.
Heat olive oil in a large skillet over medium heat. Add chicken and brown on all sides, about 4 minutes. Add bell peppers and sauté with chicken until beginning to soften.
Meanwhile, whisk together apple cider vinegar, soy sauce, honey, ketchup and garlic. Pour sauce into the skillet. Simmer together with the meat for 5 minutes, until the chicken is cooked through and the sauce has thickened slightly.