Preheat the oven to 400 degrees F.
In a large bowl, combine the sweet potatoes, cabbage, thyme, and 3/4 teaspoon salt. Drizzle with 2 tablespoons olive oil and toss to coat. Spread the remaining teaspoon of olive oil on a 13-x-18-inch sheet pan, then spread the sweet potato mixture evenly on the pan.
Bake for 20 minutes, then remove from the oven and use a spatula to divide the mixture into six portions.
Shape each into a round nest with a divot in the center. Crack an egg into each divot, sprinkle with a bit of salt, then bake for 10 more minutes. Check that the yolk is done to your liking — you may choose to bake for a few additional minutes.
While the sweet potatoes bake, line a second sheet pan with parchment paper and lay the bacon strips on it. Bake for 12 to 20 minutes, depending on the thickness of the bacon and your desired level of crispness. Drain the bacon on paper towels, then serve each nest with a strip of bacon.