Step 1

Preheat the oven to 425°F and line an 11-by-17 inch rimmed baking sheet with parchment paper. Transfer potatoes, Brussels sprouts, shallots, and garlic to the baking sheet. Toss with 1/4 cup olive oil, salt, and pepper. Use your hands to spread everything into an even layer. Transfer to oven and roast, stirring halfway, until sprouts are crispy and potatoes are just tender, about 25 minutes. Remove from oven.

Step 2

Meanwhile, strip kale from its stems, tear leaves into bite-sized pieces, and toss with remaining tablespoon of olive oil and a pinch each salt and pepper. Add to baking sheet and stir into the potato and Brussels sprout mixture. Crack the eggs over the mixture and return to oven until whites are set, 7 to 9 minutes (the shorter end of this time will yield runny yolks, while the longer end will result in firm yolks). Season with salt, pepper, and crushed red pepper. Serve warm.