Heat the olive oil in a skillet over medium heat. Season the chicken breasts with salt and black pepper. Put the milk into a shallow bowl and the breadcrumbs into another shallow bowl. Dip the chicken into the milk and then dredge in the breadcrumbs. Place in the hot oil. (You could use boneless chicken thighs instead of chicken breasts.)
Cook the chicken until golden brown on the first side. Flip the chicken over and continue to cook until the other side is golden brown. You have two options here: 1) Cook the chicken all the way through and remove to a plate. Tent with foil to keep it warm. 2) Cook the chicken until it is almost cooked through, remove to a baking dish and pop it into a 300-degree F oven to stay warm and finish cooking while you make the sauce.
To make the basil cream sauce, in the same pan, add the garlic. Cook, stirring, for 30 seconds. Pour in the chicken broth and bring to a boil. Stir to remove any brown bits from the bottom of the pan. Add the heavy cream and bring to a boil. Add the basil, Parmesan cheese, salt and black pepper to taste. Reduce the heat and cook, stirring often, until it thickens a bit, about 3 to 5 minutes.
To serve, spoon the sauce over the chicken breasts.
