Wash and dry all produce. Adjust rack to middle position and preheat oven to 450 degrees. Halve, peel, and mince shallot. Trim, then thinly slice scallions, keeping greens and whites separate. Cut sweet potatoes into 1/2-inch-thick wedges.

Toss sweet potatoes on a baking sheet with a drizzle of oil, salt, and pepper. Roast in oven until tender and crisped, about 25 minutes, tossing halfway through.

Heat a large drizzle of oil in a large pan over medium-high heat. Pat pork dry with a paper towel. Season all over with salt, pepper, and half the Italian seasoning (use the rest as you like). Add to pan and cook to desired doneness, 3-5 minutes per side. Remove from pan and set aside to rest on a plate.

Lower heat under pan to medium low. Add 2 TBSP butter and let melt. Toss in shallot and scallion whites. Cook until softened, about 2 minutes. Sprinkle in flour and stir until lightly toasted, about 1 minute. Slowly whisk in 1 cup milk (we sent more). Simmer gently until thickened, 1-2 minutes. Stir in demi-glace and 1/2 cup water. Continue simmering until saucy, 1-2 minutes. Season with salt and pepper. Remove from heat.

While pork and gravy cook, place broccoli in a medium, microwave-safe bowl and add a splash of water. Cover with plastic wrap and poke a few holes in wrap. Microwave on high until just tender, about 2 minutes. Remove wrap, pour out any water left in bowl, and sprinkle cheddar over broccoli. Microwave again until cheese melts, about 1 minute more.

Stir any juices released by pork into gravy. Divide sweet potatoes, broccoli, and pork between plates. Spoon gravy over pork. Sprinkle with scallion greens and serve.