Step 1 Position racks in the top and bottom thirds of the oven and heat oven to 450 degrees.
Step 2
On a large sheet pan, arrange the mushrooms, sweet potato, red onion and kale into four separate quadrants. Drizzle the vegetables with 3 tablespoons of the olive oil, season with salt and pepper, and toss to coat, keeping the types of vegetables separate. Try to not crowd the vegetables; you want them to brown, not steam. Roast on the top rack until the sweet potato is fork-tender, the onion and mushrooms are slightly caramelized and the kale is crispy but not burnt, 20 to 25 minutes.
Step 3
Meanwhile, place another large sheet pan on the bottom rack to heat. When the vegetables are almost done cooking, in the last 5 minutes or so, remove the heated pan from the oven and evenly drizzle the remaining 3 tablespoons of olive oil on it. Spread the rice over half of the pan. Crack the eggs onto the other half and carefully transfer to the oven. Bake until the whites are just set and the yolks are still runny, 3 to 6 minutes (this time may vary depending on your oven, so watch it
carefully).
