In a large frying pan with a lid, warm one tablespoon of olive oil over medium heat. Add the crumbled chestnuts and sauté for 6-7 minutes, stirring occasionally, until they develop a golden hue and crisp edges. Remove them from the pan and place on a plate lined with kitchen paper to drain. Meanwhile, combine the harissa paste with the natural yogurt in a small bowl, season to taste, and set aside.
Pour the remaining olive oil into the pan, then scatter in the cumin seeds. Cook them gently until aromatic, ensuring they do not burn. Stir in the sliced red onion and cook for about 10 minutes, or until softened, stirring occasionally. Add the minced garlic and sliced chili, cooking for an additional 2 minutes to release their flavors.
Increase the heat to medium and toss in the shredded Brussels sprouts. Cook for 8-10 minutes, stirring frequently, until they begin to soften. Fold in the spinach and allow it to wilt, then season the mixture to taste.
Reduce the heat to medium-low and create four small wells in the sprout mixture. Crack an egg into each well, cover the pan with a lid or foil, and cook gently for 5-8 minutes, or until the egg whites are fully set but the yolks remain slightly runny.
To serve, drizzle the harissa yogurt over the dish and sprinkle with the crispy chestnuts. Offer the remaining harissa yogurt on the side.