Place an oven rack on the center shelf and preheat the oven to 425 degrees F. Line a large sheet pan with foil.
In a medium-sized bowl, toss the broccoli with olive oil, salt and pepper. Spread in a single layer on half the pan. Cook for 12 minutes.
While the broccoli is cooking, prepare the shrimp. In a liquid measuring cup, whisk together the honey, soy sauce, sambal or pepper flakes, and garlic. Pour into a resealable plastic bag, add the shrimp, and toss to combine (you don’t technically have to use the bag; a bowl is also fine).
After 12 minutes, remove the broccoli from the oven and turn the florets over using spatula or tongs.
Lightly spray the other side of the sheet pan with cooking spray (or brush with a thin layer of olive oil). Add the shrimp in a single layer and cook for and additional 8-12 minutes, until the shrimp is opaque (the time will vary based on the size of the shrimp, so I recommend turning on the oven light and keeping an eye on them toward the end).
While the shrimp is cooking, place the cornstarch in a small saucepan. Whisk in a few tablespoons of the marinade until smooth, then whisk in the remaining marinade. Cook over medium heat, whisking frequently, until the sauce thickens, about 5 minutes. If the sauce becomes too thick/reduced for your preference, whisk in 1-3 tablespoons of water, or however much you need to reach the desired texture.
Serve the shrimp and broccoli over rice, your favorite grain, or on its own. Top with the sauce and garnish with sliced scallions and toasted sesame seeds, if using.
I buy bags of frozen shrimp that are already peeled and deveined. Costco has jumbo frozen shrimp (which are hard to find) at a very reasonable price. To thaw them out quickly, place in a colander in the sink under cool running water for around 5 minutes.You can leave the tails on or remove them before cooking. Leaving the tail on while cooking prevents that side of the shrimp from drying out since it finishes cooking first.