This tender pork loin simmers in its own succulent sauce, flavored by onions and herbs. It's a perfect weekend cooking project for a special Sunday Dinner. The sauce isn't pretty, but you won't care. Any leftovers are fantastic during the week. Mashed potatoes, polenta, or even rice would be a lovely accompaniment.
Set a large (~8-qt.), heavy-bottomed Dutch oven over medium-high heat. Add the butter and oil. When the butter has melted and begins to foam, add the pork, browning on all sides (including ends, 8-10 minutes). Remove the pork to a plate.
Reduce the heat to medium. Add the olive oil to the pot along with the onion. Sauté until fragrant and slightly translucent, about 1 minute.
Return the pork to the pot—fat cap up—along with any juices that have accumulated on the plate. Add the herbs (except the sage) and garlic. Pour the milk over the top of the meat. Arrange the sage leaves on top of the fat cap. Raise the heat to medium-high to bring to a simmer, then reduce heat to maintain a gentle simmer. Lid the pot so that it's slightly cracked. Simmer, undisturbed, for 45 minutes.
Check the temperature of the meat by inserting an instant-read thermometer into the thickest part. Continue simmering (partially lidded) until the meat reads 142 degrees F. Remove pork to a carving board, cover with foil, and allow it to rest for up to 30 minutes (minimum 15). Discard the sage.
Remove any herb sprigs and large leaves from the pot along with the garlic clove. Discard. Simmer the liquid in the uncovered pot until it has reduced by two-thirds and you see golden-brown curds throughout sauce (~10 minutes). Season to taste with salt and pepper.
Slice the roast into 1/3"-1/2" slices and arrange on a platter. Ladle the sauce over the top and serve.
You can tie the herbs into a bouquet with kitchen twine if you'd like (leave the sage leaves out to place on top of the pork, and leave the bay leaf free).