Begin by preheating your oven to 350 degrees Fahrenheit.
Rub the pork loin with olive oil and season generously with salt and pepper. Heat a cast-iron skillet over medium-high heat.
Cut small strips into the sides of the pork loin to prevent it from curling in heat and to ensure even cooking.
Heat a cast-iron skillet over medium-high heat. Once the skillet is hot, add the unsalted butter, minced garlic, and chopped sage leaves. Let them melt and infuse their flavors into the butter, creating a fragrant base for searing the pork loin.
Drop on the pork loin and sear for 2-3 minutes on each side until it develops a golden-brown crust.
Transfer the skillet to the oven and roast the pork loin for 20-25 minutes, or until it reaches an internal temperature of 145°F.
(Bonus)Deglazing the Pan
While the skillet you used for the pork is still hot, deglaze it by adding chicken broth and lemon juice. Use a spatula to scrape up any browned bits from the bottom of the pan, incorporating them into the liquid.
After deglazing the pan, allow the chicken broth and lemon juice mixture to simmer over medium heat.
Let it cook for a few minutes until it reduces slightly, concentrating the flavors.
Cut the cold unsalted butter into small cubes and set aside.
Once the liquid has reduced, drop heat to low and whisk in the cold butter, one cube at a time.
Whisk continuously until each cube of butter is fully melted and incorporated into the sauce.
Taste the sauce and adjust the seasoning if necessary with salt and pepper.