Using butcher twine, wrap around the loin, about every inch, and tighten it firmly. Cut off any excess twine with shears. (This step is optional, but it allows the meat to cook evenly by maintaining a consistent shape.)

To make the brine, combine the cider, water, salt, peppercorns, brown sugar, garlic cloves, chopped rosemary, and herbs de Provence in a deep bowl and whisk together. Place the loin in a container and add the brine. The container should be small enough that the loin is completely covered with the brine. If it is not, add a little more water.

Wrap the loin container tightly and refrigerate for 12 hours. Remove the loin from the brine, rinse off, and pat dry. Let rest at room temperature for 30 minutes before cooking. If not cooking right away, store in refrigerator.

Preheat oven to 375°F.

Warm a large heavy-bottom sauté pan on medium high heat. Add the vegetable oil and place the loin in the center. Sauté for 5 minutes or until all sides are evenly browned.

Add the butter and rosemary, and reduce heat to a simmer. Baste the melted butter and rosemary over the loin for 3–5 minutes or until the butter starts to brown. Remove the loin from the pan and place on a baking sheet.

Pour the browned butter and rosemary over the loin, and place the baking sheet in the oven. Cook for 15–20 minutes or until the internal temperature reads 145°F using a meat thermometer. Rest on a cutting board for 3–5 minutes, slice, and enjoy.