Pat the pork loin completely dry with paper towels. Season all over with 1.5 tsp fine sea salt and 0.5 tsp black pepper, pressing the seasoning into the surface.

Heat the butter and olive oil in a 5-quart Dutch oven over medium-high heat until the butter foam subsides. Add the pork and sear on all four long sides until deep golden brown, about 3 to 4 minutes per side. Transfer the pork to a plate.

Reduce the heat to medium. Add the crushed garlic cloves and sage leaves to the pot and cook for 1 minute until fragrant, stirring once.

Pour in the milk and add the lemon zest strip. Stir gently and scrape up any browned bits from the base of the pot.

Return the pork to the pot. The milk should come at least halfway up the sides of the loin. Bring to a gentle simmer, then reduce the heat to low. Set the lid on at a slight angle so a little steam can escape.

Braise for 70 to 80 minutes, turning the pork once at the halfway point. Do not stir the milk. As the liquid reduces, the milk will begin to curdle and form small golden-brown clusters. This is correct.

Check doneness with an instant-read thermometer. The pork is ready at 65 to 68 C (150 to 155 F) at the thickest point. If the curds are still pale, remove the pork and cook the sauce over medium heat for 5 more minutes until they turn nutty amber.

Transfer the pork to a cutting board and rest for 10 minutes. Remove and discard the lemon zest strip. Taste the pan sauce and adjust salt.

Slice the pork into 1.5 cm rounds. Return the slices to the pan sauce for 2 minutes to warm through, then plate with the golden milk curds spooned generously over the top.