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Heat a grill to medium.
Cut off the stem end of the Brussels sprouts and remove any yellowing outer leaves. Place the Brussels sprouts into a large, microwave safe mixing bowl and heat in the microwave on high for 3 minutes. Add the olive oil, garlic, mustard, paprika and salt and toss to combine. Allow the sprouts to cool until you can handle them. Skewer 4 to 5 Brussels sprouts onto each metal skewer with the stem ends facing in the same direction, leaving at least 1/2-inch in between each sprout. Place the skewers onto the grill with stem end closest to the flame. Cover and cook for 5 minutes. Turn the skewers over and continue to cook for another 5 minutes. Serve as is or for additional flavor, remove the sprouts from the skewers, return them to the original mixing bowl and toss with any of the remaining oil and garlic mixture before serving.