Adjust rack to top position and preheat oven to 450 degrees. Bring a large pot of salted water to a boil. Wash and dry produce.

Cut broccoli into 1-inch pieces if necessary. Zest and quarter lemon. Peel and mince or grate garlic.

Toss broccoli on a baking sheet with a drizzle of olive oil, salt, and pepper.

Roast on top rack until browned and crispy, 12-15 minutes.

Once water is boiling, add spaghetti to pot. Cook, stirring occasionally, until al dente, 9-11 minutes.

Reserve ½ cup pasta cooking water (1 cup for 4 servings), then drain.

While pasta cooks, place 3 TBSP butter (6 TBSP for 4 servings) in a small microwave-safe bowl. Microwave until just softened, 10 seconds. Add lemon zest, half the Parmesan (save the rest for serving), a pinch of garlic, and a pinch of chili flakes if desired. Mash with a fork to combine. Season with salt and pepper.

Rinse shrimp* under cold water, then pat dry with paper towels. Toss in a large bowl with a large drizzle of olive oil, remaining garlic, salt, and pepper.

Heat a large pan over medium-high heat. Add shrimp and cook, stirring occasionally, until opaque and cooked through, 2-4 minutes.

To pan with shrimp, add drained spaghetti, broccoli, stock concentrate, garlic butter, and ¼ cup reserved pasta cooking water (⅓ cup for 4 servings). Toss until everything is thoroughly coated in sauce. Add a squeeze or two of lemon juice to taste. Season with salt and pepper.

Divide pasta between bowls and top with remaining Parmesan and a pinch of chili flakes if desired. Serve with any remaining lemon wedges on the side.