Rub garlic, oregano, salt and pepper all over the chicken breasts and set aside for ten minutes.
Heat butter and olive oil in a cast iron skillet, and add the chicken to the pan. Cook for 4-5 minutes on each side or till cooked through and no longer pink based on the size of the breasts. Once the chicken is cooked, transfer it to a plate and cover loosely with foil.
In the same pan, heat the remaining butter and olive oil for the sauce and add the garlic. Saute the garlic for a minute till fragrant and add the flour. Cook the flour for a minute and slowly start whisking in the milk till the sauce thickens.
Simmer the sauce for 2-3 minutes and add the oregano, basil, salt and pepper. Stir everything together and add the chicken breasts back to the pan. Simmer the chicken in the sauce for 2 minutes and turn off the flame. Serve hot.