Preheat oven to 450°F/230°C, combi steam. If your oven has variable steam settings, use 50%. If not, don’t worry! Just set to combi steam at the correct temperature and the oven will take care of the humidity.
Put the broccoli onto a sheet pan and drizzle with the oil. Spread into an even layer and roast for 6 minutes.
1 lb broccoli, 1 Tbsp vegetable oil
While the broccoli starts cooking, whisk the soy sauce, ginger, chili bean paste, wine, sesame oil and sesame seeds together in a large bowl. Gently toss the shrimp through this mixture and set aside.
When the timer goes off for the broccoli, add the shrimp and soy sauce mix to the pan, tucking the shrimp around the pieces of broccoli so everything remains in a single layer. Drizzle over any sauce that remains in the bowl and return to the oven until the shrimp are just opaque and the broccoli is tender, about 5 minutes.
Serve the shrimp and broccoli hot (with steamed rice if you like).
Notes
Dark soy sauce has a deeper flavor and color than regular or light soy sauce. You can use regular/light soy; the final color of the dish will be lighter.
Chili bean paste is a fermented chili, bean and garlic paste available from Asian supermarkets. It adds lovely heat and depth to all sorts of marinades and sauces. If you can't find it, substitute regular chili paste or minced fresh chili pepper and a clove of mince garlic.
Shaoxing, or Chinese cooking wine, is found in Asian supermarkets. Dry sherry makes a great substitute.
Use fresh or frozen shrimp, it's up to you. Frozen shrimp should be thawed first, on a paper towel in a single layer. Size is also up to you; just allow an extra minute or two of cooking for very large shrimp. If you are buying whole (unpeeled) shrimp, you'll need about 30-40% more by weight to allow for the removal of the heads and shells (see main post for peeling and deveining details).
Variations to make different sheet pan shrimp dinners:
Healthy garlic shrimp: Omit the sauce ingredients and replace with 2 tablespoons of garlic butter. This is far less butter than a traditional garlic shrimp recipe uses, but you get all the flavor. Leave the broccoli in, or omit if you just want straight up garlic shrimp. Add a quarter cup of chopped parsley to the shrimp as it comes out of the oven for a classic garlic shrimp flavor.
Shrimp in chili garlic sauce: Make a gorgeous baked chili garlic shrimp instead of my soy ginger version! Omit the sauce ingredients in the recipe and replace with 1-2 fresh red chili peppers and 3 cloves garlic. Mince the chili and garlic and mix with 2 tablespoons olive oil before tossing with the shrimp. At the end of cooking, stir 3 tablespoons heavy cream through the shrimp.
Lemon pepper shrimp: For a really fast lemon pepper shrimp, use store bought lemon pepper seasoning. This is great with the broccoli (did you know broccoli loves lemon?!). Omit the sauce ingredients and instead toss the shrimp in 2 tablespoons lemon pepper seasoning and a half teaspoon of garlic powder before cooking.