Set the flour, eggs and panko in three separate shallow bowls. Season the chicken cutlets with salt and pepper. Dredge the chicken in the flour, shaking off any excess, then dip in the eggs and coat thoroughly with the panko, pressing lightly to adhere.
In each of 2 large skillets, heat 1/4 cup of canola oil. Add the chicken and cook over moderately high heat, turning once, until golden and crispy, about 3 minutes. Transfer the chicken to a paper towel-lined baking sheet and sprinkle with salt.
Meanwhile, in a small saucepan, melt the butter and cook over moderately high heat until browned and nutty, about 4 minutes. Stir in the capers, lemon juice and parsley; spoon over the chicken and serve.