Heat oil over medium-high in a large, heavy-bottomed pot with a lid, such as a Dutch oven, big enough to hold your roast. Season roast with salt and pepper. Place top/fat-side down into the pan and allow to cook until golden. Flip over roast and allow to cook another few minutes. Add garlic cloves and shallots to the pan and stir around the pan a minute or so to soften (watch closely so they don't scorch).
Add wine to pan and allow to boil for a minutes, then reduce heat to medium-low, placing the lid over-top slightly ajar, so that pot is not completely covered. Cook for 20 minutes, flip roast and stirring, making sure there is liquid in the pan that is at a gentle simmer. Continue cooking, flipping and checking every 20 minutes, for a total of about 1 1/2 hours, adding more wine if necessary if pan gets dry, or until the roast internal temperature reaches 135-140 degrees when tested with a thermometer. Remove roast to a cutting board and tend loosely with foil.
To the pan, add chicken broth, heavy cream, Dijon and tarragon. Bring to a simmer, stirring pan to loosen any brown bits on the bottom of the pan. Season with salt and pepper. If necessary, thicken sauce by stirring together water and cornstarch and adding a bit at a time to the gravy until sauce thickens as much as you'd like.
Keep sauce warm. Cut pork away from bone in one large piece and thinly slice to serve with gravy or alternately, cut down through the roast and bone into thicker chops and serve drizzled with sauce.
Notes
A pork loin is different from a pork tenderloin. A pork loin is large and thicker. The cooking times listed here are for a bone-in pork loin roast. A boneless pork loin roast will work, though you should expect the cooking time to be less. If you want to try this recipe with a smaller, thinner pork tenderloin, the cooking time will be considerable less, in the 35-40 minute range. Test often with a thermometer to test for doneness.Be sure to read the notes above this Recipe Card, for more tips, options, substitutions and variations for this recipe!