Preheat oven to 400°F (205°C). Line large 12 x 17-inch (30 x 43 cm) rimmed baking pan with parchment paper.
Place sweet potatoes, onion, and peppers on pan. Drizzle with olive oil and sprinkle with thyme, salt and pepper; toss to combine. Spread out in single layer. Bake until sweet potatoes are tender, about 15 minutes.
Add sausages and kale to the pan. Bake for 5 minutes, or until kale starts to soften and wilt.
Remove pan from oven. Using back of a spoon, make 6 wells in the vegetables; gently crack 1 egg into each. Bake until egg whites are set, about 7 minutes. Gently shake baking sheet to check softness of yolks. If hard yolks are desired continue to bake for an additional 5 minutes.
Garnish with parsley or crumbled feta cheese, if desired.
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