Your question is a little tricky since I can only go by your description. I’d suggest bringing a leaf with the sample eggs to one of the Hewitts locations for a positive ID. Having said that, I make an educated guess that you probably have Squash Bug eggs on your brussel sprouts. The easiest way to control them is to remove and discard the eggs before they hatch. Once they hatch, the beetles can be controlled with insecticidal soap or other contact killer rated for use in the vegetable garden. Here’s a link for more information on Squash Bugs http://www.planetnatural.com/site/xdpy/kb/squash-bug-control.html There are other insects that may attack your brussel sprouts. Here’s a helpful link to identifying them. http://www.harvestwizard.com/2009/06/brussels_sprouts_growing_probl.html