Sprinkle a small amount of water on a large sheet of plastic wrap. Place 2 of the breast halves on top of the plastic and sprinkle again with water. Cover with another sheet of plastic wrap and pound with a rolling pin or meat pounder until about 1/4-inch thick. Repeat with the remaining 2 breast halves.

Mix the flour with the salt and pepper in a shallow pie plate. Heat half the butter in a large skillet over medium-high heat until hot. Working in 2 batches, place the chicken in the flour mixture and turn to coat on all sides. Shake off the excess flour and add to the skillet. Cook until lightly browned, 3 to 4 minutes per side. Transfer to a plate or platter and cover loosely with foil. Repeat with the remaining butter and chicken.

Add the shallot and garlic to the skillet. Cook, stirring, until fragrant, about 30 seconds. Add the tomatoes or salsa, stir in the stock, and simmer for 8 minutes. Return the chicken to the skillet and simmer, turning often, until the chicken is warmed through and the sauce is thickened, about 2 minutes. Transfer the chicken to warm serving plates. Stir in the basil and season the sauce with salt and pepper. Spoon over the chicken and serve at once.