Preheat oven to 400°F. Line a baking sheet with parchment paper.
Whisk the hoisin, soy, honey, vinegar, Dijon, ginger, sesame oil, garlic, and chili flakes together in a small bowl. Whisk in the vegetable oil.
In a large bowl, toss the broccoli and onions with about half of the sauce. Transfer to baking sheet. Bake 20 minutes.
In the meantime, toss the shrimp in the remaining sauce and let marinate. Remove baking sheet from oven and arrange shrimp on it. Return to oven for an additional 15 minutes, until shrimp are cooked through. Serve on white rice.
