How to Make It
Chop off the ends of the sprouts. Slice them in half, then finely chop each half. Place the shreds in a bowl—you should end up with about 4 cups—and sprinkle with salt and pepper.
Melt the butter in a medium-size nonstick pan with a lid over medium-high heat, swirling to coat the pan. Add the Brussels sprouts and the garlic, then let them cook until just a little wilted, about 1 minute. Toss the mixture. Add the olives and toss again.
Crack the eggs into the pan so they aren’t touching. Sprinkle with salt and pepper. Pour in 2 tablespoons water and cover with the lid. Let the eggs steam, undisturbed, until the whites are cooked through but the yolks are still runny, about 2 minutes.
Turn off the heat and squeeze lemon juice over everything. Serve immediately.