Caramelize onions: Peel and thinly slice onion; finely chop 2 tablespoons of the onion. Heat 1 tablespoon oil in a medium skillet over medium-high. Add sliced onions, ½ teaspoon sugar, and a pinch each of salt and pepper. Cook, stirring often, until browned; add 1 tablespoon water to scrape up browned bits, every so often, 12–15 minutes. Transfer to a bowl. Wipe out; reserve skillet for step 4.
Make vinaigrette: Meanwhile, bring a medium saucepan of salted water to a boil. Coarsely chop capers. Pick tarragon leaves from stems, discard stems and finely chop 1 tablespoon leaves. In a medium bowl, stir to combine chopped tarragon, chopped onions, capers, 2 tablespoons oil, and 1 tablespoon vinegar. Season to taste with salt and pepper.
Cook green beans: Trim green beans, then cut into 1-inch pieces. Add to boiling water and cook until bright green and crisp-tender, about 3 minutes. Using tongs, transfer green beans to bowl with vinaigrette, and toss to coat. Season to taste with salt and pepper. Reserve the saucepan with water for step 6.
Cook pork: Pat pork chops dry and season all over with 1½ teaspoons steak seasoning. Heat 1 tablespoon oil in a reserved skillet over medium-high. Add pork and cook until well browned, but not cooked through, about 2 minutes per side. Transfer to a plate. Pour off and discard any fat.
Make sauce: Return caramelized onions to skillet; stir in broth concentrate, ¾ cup water, and 1 teaspoon vinegar. Return pork chops to skillet. Bring sauce to a simmer and cook over medium-high, turning chops halfway through, until sauce is thickened and chops are cooked through, about 5 minutes. Swirl in 1 tablespoon butter. Season to taste with salt and pepper.
Cook noodles & serve: While sauce simmers, return water in saucepan to a boil; add noodles and cook until tender, about 6 minutes. Drain, return to the saucepan, and toss noodles with 1 tablespoon butter. Season to taste with salt and pepper. Spoon noodles onto plates, then top with pork chops and sauce. Serve green beans alongside.