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Step 1
Bring a large pot of salted water to a boil. Add the spaghetti and cook as the label directs for al dente, adding the broccoli in the last 2 minutes of cooking. Reserve 1/2 cup cooking water, then drain the pasta and broccoli and return to the pot. Add 1 tablespoon butter, 2 tablespoons parsley, the lemon zest and a big pinch each of salt and pepper. Stir well, adding the reserved cooking water as needed to loosen.
Step 2
Meanwhile, season the pork chops on both sides with salt and pepper. Dust with the flour, shaking off any excess. Heat the olive oil in a large skillet over medium-high heat. Add the pork chops and cook until well browned and just cooked through, about 4 minutes per side. Remove to a plate and tent with foil to keep warm.
Step 3
Carefully add the wine to the skillet, scraping up the browned bits from the pan. Cook until reduced by about half, then stir in the lemon juice and capers; return to a simmer. Remove from the heat and swirl in the remaining 2 tablespoons each butter and parsley until the butter is melted. Pour in any accumulated juices from the plate of pork. Season the sauce with salt and pepper.
Step 4
Divide the spaghetti and broccoli among plates and top each serving with a pork chop. Spoon the sauce on top.