Preheat oven to 425 degrees.
In a large bowl, toss broccoli with 2 tablespoons oil, coriander, cumin, chili powder and a generous pinch of salt and pepper. In a separate bowl, combine shrimp, remaining 2 tablespoons oil, lemon zest, and a generous pinch of salt and pepper.
Spread broccoli in a single layer on a baking sheet. Roast for 10 minutes. The broccoli will be just starting to brown. Add shrimp to baking sheet and toss with broccoli. Roast, tossing once halfway through, until shrimp are just opaque and broccoli is tender and golden around edges, about 10 minutes more.
Squeeze lemon juice over shrimp and broccoli just before serving.