Bring a large pot of water to a rolling boil; salt it well. Cook the chickpea rotini according to package directions until just al dente, usually 7–9 minutes. Reserve 1 cup of the starchy pasta water, then drain. (Chickpea pasta foams more than wheat pasta — use a big pot and don't walk away.)

While the pasta cooks, pat the shrimp very dry with paper towels and season with the salt and pepper. Dry shrimp sear instead of steam.

Heat 2 tablespoons of the olive oil in a large skillet over medium-high heat until shimmering. Add the shrimp in a single layer and cook about 2 minutes per side, until pink, opaque, and just curled into a C shape. Transfer to a plate — they finish in the sauce.

Reduce the heat to medium. Add the remaining 1 tablespoon olive oil and 2 tablespoons of the butter to the skillet. Stir in the sliced garlic and red pepper flakes; cook 60–90 seconds, until the garlic is golden at the edges but not brown.

Pour in the white wine (or broth), scraping up the browned bits. Simmer 1–2 minutes, until reduced by about half and no longer harsh.

Add the drained pasta to the skillet along with 1/2 cup of the reserved pasta water, the lemon zest and juice, and the remaining 2 tablespoons butter. Toss vigorously until the butter melts into a glossy sauce that clings to the rotini, adding splashes of pasta water as needed. Return the shrimp and any juices to the pan; toss 30 seconds to warm through. Shower with parsley and Parmesan and serve immediately with lemon wedges.