Season the pheasant breasts on all sides with salt and pepper. Sprinkle the flour onto a plate, and press the pheasant breast into the flour until completely coated. Shake off excess flour and set aside. Melt the butter in an ovenproof Dutch oven or deep skillet over medium heat. Cook the pheasant breasts in the hot butter until golden brown on both sides, about 5 minutes per side. Pour in the half-and-half cream and bring to a simmer; cover the Dutch oven.
Bake in the preheated oven until the pheasant breasts are tender and no longer pink in the center, about 1 1/2 hours. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
