Prepare the Brussels sprouts: Separate the smaller sprouts and set them aside. For the large sprouts, trim off the white stems. 2-4 outer leaves will fall off of the sprouts. Set them aside in a bowl. Cut the sprouts in half. For the smaller sprouts simply trim the stem and set aside any loose outer leaves. We'll roast these ones whole.
Bake the sprouts: Add the Brussels sprouts to the baking sheet. Drizzle with 1 teaspoon of olive oil. Season with salt and pepper. Arrange the sprouts with the flat side down. Let the whole ones roast as is. Bake for 20 minutes.
The leaves: Add 1/2 teaspoon olive oil to the Brussels loose outer leaves. Season with salt and pepper. Add to the baking sheet after 20 minutes and bake for another 5 minutes.
Make the sauce: Add the sauce ingredients to a small skillet. Heat over medium heat until it comes to a boil. Turn heat down to low and let simmer for 4-5 minutes, just until thickened.
To serve: Remove the Brussels sprouts from the oven and add them to the skillet with the sauce. Mix well. Remove to a serving bowl. Sprinkle with sesame seeds and serve while hot.