Line a plate with a double layer of paper towels. Place a 10-inch non-stick skillet over medium heat and lay the bacon slices in the pan. Cook until crisp, turning every minute or so, about 4 minutes. Transfer to the prepared plate. When cooled, crumble the bacon and reserve.
Pour off some of the bacon fat, leaving enough to cover the bottom of the pan. Add the Brussels sprouts and onions and stir to coat. Add the sprouts to the pan, stir, and turn — cut side down — for 1 minute (without stirring). Cook another 3 minutes to brown, stirring occasionally. Sprinkle with salt and thyme, grind some pepper over the top, and toss to mix.
Push the vegetables to the sides to form two spaces for the eggs. Crack each egg into the pan into the spaces created. Cover the pan and reduce the heat to medium-low. Cook for about 4 minutes, until the whites are opaque, and the yolks are done to your liking.
Put a toasted English muffin on each plate and place an egg on top of the muffin, then divide the vegetables between the plates. Sprinkle with crumbled bacon and serve.