Preheat oven to 400°F.
On a half sheet pan, combine the brussels sprouts, turnips, bacon, and shallot.
Add half of the olive oil and all the thyme, garlic powder, red pepper flakes.
Toss to combine.
Roast, tossing 2 to 3 times during cooking, until vegetables and bacon are caramelized a deep golden brown and the vegetables are tender, about 25 minutes.
Meanwhile, add the remaining olive oil to a large non-stick skillet and heat over a medium heat.
Crack the eggs and add them one at a time to the pan, spacing them evenly apart.
Cook until the whites are cooked through but the yolks are still a bit runny, flipping once.
Serve the eggs over the finished hash.