Bring a large pot of salted water to a boil. Cook pasta 1 minute less than package directions for al dente. Reserve 1/4 cup pasta water, then drain pasta. Set aside.

While pasta cooks, pat shrimp dry with paper towels. Season lightly with salt and pepper.

Heat a large skillet over medium-high heat. Add 1 tablespoon butter and the olive oil. When butter foams, add shrimp in a single layer. Cook without moving for 1 minute, then flip and cook 1 minute more until just pink and opaque. Transfer shrimp to a plate (they will finish cooking in the sauce).

Reduce heat to medium. Add remaining 2 tablespoons butter, garlic, and red pepper flakes. Cook, stirring constantly, until garlic is fragrant and just golden, about 30 seconds. Do not brown the garlic — it turns bitter.

Pour in white wine and chicken broth. Increase heat to medium-high and bring to a simmer. Cook, scraping up any browned bits from the pan, until liquid reduces by about half, 3 to 4 minutes.

Stir in lemon zest, lemon juice, and the cooked pasta. Toss to coat. If the sauce seems too thick, add reserved pasta water a tablespoon at a time until it glistens.

Return shrimp to the skillet, along with any accumulated juices. Toss for 30 seconds just to warm through. Remove from heat.

Sprinkle with fresh parsley and serve immediately. Pass extra lemon wedges at the table.