Butterfly the pork loin by starting with the fat side up on a cutting board. Insert your knife ⅔ of the way up from the bottom, and carefully begin cutting horizontally.
Stop about a ½ inch from the end, and open up the flap.
Now, continue cutting down by pivoting your knife so you are cutting back in the opposite direction, about a ⅓ way down from the bottom of the roast. You are opening up the roast to make a flat piece of meat.
Fully open the flap (see pictures and/or video for reference).
Cover with plastic wrap, and pound with the side of a meat tenderizer until the roast is between ¼" to ½" thick.
Combine the brown sugar and 1 tablespoon salt in a bowl and then sprinkle all over the roast.
Transfer to a large zipper-lock bag, seal, and refrigerate for at least 1 hour, or up to 24 hours.
Preheat oven to 275 F.
Heat 2 tbsp of oil and sauté the sliced garlic cloves in an oven-safe 12-inch skillet over medium-high heat until garlic begins to brown, about 3 minutes.
Transfer garlic and oil to a separate medium-sized bowl and let cool for 5 minutes.
Stir Parmesan, parsley, basil, capers, anchovies, lemon zest, and ½ teaspoon black pepper into garlic oil.
Place roast cut side up on cutting board. Spread Parmesan mixture evenly over the surface of the roast, leaving a ½-inch border on all sides.
Starting on the short side, roll the roast tightly, and then tie with kitchen twine at 1-inch intervals. Season the roast with black pepper.
Heat the remaining 2 tablespoons of oil in the skillet over medium heat. Sear roast on all sides until browned, about 12 minutes. Flip roast, seam side down, in the skillet and add shallots, rosemary sprigs, and whole garlic cloves. Transfer to middle rack in the preheated oven.
Cook until thickest part of roast registers 135°F. (about 1 hour and 10 minutes).
Transfer roast to carving board and tent with aluminum foil...let rest for 30 minutes (Don't clean skillet, yet).
Meanwhile, use a fork to smash garlic in skillet. Place the skillet over medium-high heat and cook until shallot and garlic are sizzling.
Stir in flour and cook, stirring, for 1 minute. Add wine and cook until nearly evaporated, about 2 more minutes. Add stock and cream and bring to a boil.
Reduce heat to medium-low and simmer until the sauce has slightly thickened, about 12 minutes. Strain through a fine-mesh strainer set over small sauce pan; discard solids. Stir in the lemon juice and season with salt and pepper, to taste. Cover and keep warm.
Discard twine from roast and slice into 1/2 inch servings. Serve, and pass sauce separately.