Heat oven to 450F.
For each bag of broccoli, fashion a foil pouch with the broccoli, generous drizzle of olive oil, and a couple pinches each kosher salt and fresh cracked pepper, sealing seams well to keep in the steam while cooking. Add the pouches to the 450F oven for 15 minutes.
Layer the shrimp on a bake sheet pan. Add to the oven when the broccoli hits the 15 minute mark, then cook both 10 minutes to cook the shrimp and finish cooking the broccoli. Remove both from the oven.
While the broccoli and shrimp are cooking, prepare the sauce. Combine the vegetable stock, wine, chili paste, sesame oil, sugar, soy sauce, and pepper in a bowl. Set aside.
Heat a wok on high heat to screaming hot. Add the tablespoon vegetable oil and swirl to coat the sides of the pan. Add the garlic and ginger and saute 30 seconds until fragrant and golden. Add the vegetable stock mixture and bring to a boil. Add the dissolved cornstarch and boil ~5 minutes until thickened enough to coat the back of a wooden spoon. Remove from the heat.
Toss the cooked shrimp in the sauce. Serve over the broccoli. Top with toasted sesame seeds. Yields 5-6 servings.