Preheat your oven to 425°F.
Peel (if desired) and cut the sweet potato into 1/2-inch cubes. Toss with a drizzle of olive oil, salt, and pepper.
Spread the sweet potato cubes on a baking tray in a single layer and roast for 20-25 minutes, stirring halfway, until tender and crispy.
While the sweet potatoes roast, thinly slice the yellow onion. In a medium skillet, heat half the olive oil over medium heat and add the onions.
Cook the onions slowly over medium-low heat for about 10-12 minutes, stirring occasionally, until they turn deep golden and caramelized. Add fresh thyme during the last few minutes of cooking.
In another skillet, cook the turkey sausage over medium heat, breaking it up with a spatula until lightly browned and cooked through, about 5-7 minutes.
In the same skillet, push the sausage to the side and crack the eggs into the space. Fry or scramble the eggs, cooking until done to your liking. Season lightly with salt and pepper.
Combine the roasted sweet potatoes, caramelized onions, turkey sausage, and eggs on a serving plate. Toss gently to mix the flavors.
Serve warm and enjoy this balanced, protein-packed hash that works for any meal of the day.