Prepare the pork. Pat the pork loin dry on all sides, then place on a wire rack set on top of a small rimmed baking sheet.
Make the rosemary rub. In a small bowl, combine 3 Tbsp melted butter (you can use 3 Tbsp olive oil, if preferred), 4 grated garlic cloves, 3 Tbsp chopped fresh rosemary, 1 Tbsp Dijon mustard, 1 tsp ground fennel seeds, 1 tsp kosher salt, and ¼ tsp black pepper. Brush this all over the pork loin, coating it evenly on all sides.
Marinate the pork. Transfer to a refrigerator uncovered, then marinate for 3 hours or up to overnight.
Cook the pork. When ready to cook, place the pork loin in a large skillet or baking dish, fat side down, then allow to sit out at room temperature for at least 20 minutes. Preheat an oven to 425°F (220°C). When ready, drizzle with 2 Tbsp extra virgin olive oil, then place into the oven. Close the door, then immediately drop the temperature to 375°F (190°C). Cook for 20 minutes, then carefully remove and flip the pork over. Return to the oven and cook for an additional 20-25 minutes, until the pork reaches an internal temperature of 145°F (63°C). Transfer the pork to a cutting board, then cover loosely with aluminum foil.
Make the sauce. Carefully place the hot skillet over medium heat. Add 1 chopped shallot, then cook, stirring occasionally, until softened, about 3-4 minutes. Increase the heat to medium-high, then whisk in ⅔ cup dry white wine, being sure to scrape any browned bits off the bottom of the pan. Add ½ cup chicken stock, then whisk in ½ tsp Dijon mustard.
Cook the butter beans. Add 3 cans of drained butter beans, then cook over medium heat until warm, about 4-6 minutes. Turn off the heat, then add 4 Tbsp unsalted butter. Carefully stir or swirl the pan until the butter has melted, being careful not to break the beans too much. Taste and adjust seasoning as needed.
Serve! Cut the pork loin into slices about ½-inch thick. Spoon some of the butter beans onto each plate, then serve with a couple slices of pork loin on top. Finish with a sprinkle of flaky sea salt, then enjoy!