In a large sauté pan, add two to three teaspoons extra virgin olive oil. Season the oil with salt and freshly ground black pepper.
Turn on the stove to medium high heat. Immediately lay the Brussels sprouts, cut side down in the pan. Be sure they are in a single layer.
Pour in the water. Cover the pan with a tight lid. Lower the heat to medium. Steam the sprouts for 3 to 4 minutes.Note: Be sure that the sprouts don't burn. Turn off the heat. Transfer the Brussel sprouts to a bowl or plate.
Add the remaining olive oil. Turn on the heat to medium.
Add the shallots and sauté 1 to 2 minutes.
Add the garlic, capers and dill. Stir and cook 30 to 60 seconds until fragrant.
Add back the Brussels sprouts. Season with salt ad freshly ground black pepper to taste. Mix to coat the sprouts with the aromatics. Turn off the stove.
Serve with your favorite main dish.