Step 1: Preheat your oven to 400°F (200°C).
Step 2: Wash and cut the broccoli into bite-sized florets.
Step 3: In a large mixing bowl, combine the broccoli florets with 2 tablespoons of olive oil, kosher salt, and black pepper. Toss until evenly coated.
Step 4: Spread the broccoli in an even layer on a large sheet pan.
Step 5: In the same mixing bowl, add the shrimp along with the remaining tablespoon of olive oil, salt, and pepper. Toss to coat.
Step 6: In another bowl, whisk together the peanut butter, soy sauce, rice vinegar, brown sugar, chili garlic sauce, lime juice, grated garlic, and ginger. Adjust consistency with warm water as needed.
Step 7: Add the shrimp to the peanut sauce and mix until well-coated.
Step 8: After 10 minutes of roasting, add the shrimp over the broccoli.
Step 9: Roast for an additional 10-12 minutes, until shrimp are pink and broccoli is tender.
Step 10: Remove from oven and garnish with sesame seeds and green onions. Serve immediately.