Season pork loin with salt and pepper. Heat oil and butter in a large pot over medium-high heat and brown pork loin on all sides. Slowly pour the milk in with the pork. Stir in the rosemary and garlic. Allow the milk to come to boil, then lower the heat to medium-low. Partially cover with the lid and cook until the pork is no longer pink in the center, about 1 hour and 45 minutes. An instant-read thermometer inserted into the center should read 145 degrees F (63 degrees C). Remove pork and set aside to rest.
If the milk is not already a nutty brown color, increase the heat until the milk beings to brown. Spoon off any additional fat. Pour the water into the pan, and bring to a boil while scraping the browned bits of food off of the bottom of the pan with a wooden spoon. Slice the pork and serve with the milk sauce.