Place a roasting pan in oven; preheat to 450°. Cut shoulder into four 1"-thick steaks; season with salt. Whisk ginger, garlic, 1 Tbsp. vinegar, and 1 Tbsp. soy sauce in a small bowl. Set both aside.
Remove stalk from broccoli. Peel, trim, and slice into ¼"-thick planks. Divide broccoli into large florets. Blanch stems and florets in a large saucepan of boiling salted water until bright green, about 10 seconds. Transfer to a rimmed baking sheet; let cool. Pat dry and toss in a medium bowl with shallots, olive oil, and sesame seeds; season with salt.
Heat vegetable oil in a large skillet, preferably cast iron, over medium-high. Cook reserved pork, undisturbed, until deep golden brown underneath, about 5 minutes. Turn and cook until an instant-read thermometer inserted into the thickest part registers 135°–140° for medium, about 3 minutes. Transfer to a cutting board and let rest 10 minutes.
Pour off fat from skillet and cook pineapple, tossing often and adding a splash or so of water if needed to keep mixture saucy, until slightly softened and browned in spots, about 3 minutes. Add 1 Tbsp. butter along with any pork juices on cutting board; toss until sauce is glossy and emulsified. Stir in remaining 2 tsp. vinegar and soy sauce. Season with salt.
Meanwhile, transfer broccoli mixture to hot roasting pan. Roast until lightly browned but still crisp-tender, 8–10 minutes. Add to reserved dressing and toss to coat; season with salt. Serve pork with pineapple and broccoli.
A special thank you to https://www.bonappetit.com/recipe/pork-shoulder-with-pineapple-and-sesame-broccoli for this delicious recipe!