My recipe for Asparagus and broccoli florets too is a fairly good amount of fresh squeezed lemon juice ( usually 2 lg. lemons - per lb of produce), some minced garlic, salt and pepper to taste.
Add the broccoli or asparagus to a 1 gal. zip lock bag along with the above mixture. Shake occasionally - to insure distribution of flavors.When nearing the end of the cook for the entree- drain liquid, and place veggies on frog mats - or in a grill basket. Cook until done to your liking. With broccoli - I like to see a bit of blackening on the tips.