Fill a bowl with 6 cups cold water and 3 tablespoons kosher salt. Add chicken pieces. Mix well. Let chicken sit in brine for 30 minutes.
In a small bowl, mix chili powder, garlic and onion powders, cumin, salt, pepper and red pepper flakes until well blended. Set aside.
Drain the brine from the bowl and pat the chicken pieces dry. Add chicken pieces to a large bowl. Sprinkle chicken with the Mexican spice mix. Pour the lime juice over the chicken and with your hands or a rubber spatula, toss the chicken pieces into the spice blend until well coated. Cover and refrigerate for 30 minutes.
Melt two tablespoons butter and olive oil together in a large skillet over medium-high heat. Add the chicken in small batches and saute 5-7 minutes, or until cooked through and no longer pink inside, stirring often. Repeat with remaining chicken pieces. Remove all chicken to a plate.
Add the garlic and remaining two tablespoons butter to the skillet and cook over medium heat just until fragrant, about 1 minute, stirring constantly. Remove the skillet from the heat and add the chicken pieces, tossing in the butter until evenly coated. Sprinkle with parsley, if desired. Serve warm.
