Bring pot of water fitted with a steamer insert to a boil.
Peal the broccoli stems then cut the heads lengthwise into quarters. Stem the broccoli for 5 minutes or until bright green color. Remove the broccoli to a large bowl and toss with salt and pepper and 2 tablespoon of the olive oil.
Using blender, mix lemon juice, anchovies, rosemary, 1/2 cup olive oil, salt and pepper to taste and blend until smooth texture. Set aside.
Now grill your broccoli over high heat, turning few times, for about 5 minutes. Transfer to a large plate and drizzle with anchovy dressing. Serve with left over dressing.