Establish the Aromatic Base : In your skillet, heat the extra virgin olive oil over medium heat. Add the diced onion and sauté for 4-5 minutes until softened and translucent. Stir in the minced garlic and cook for another minute until fragrant, being careful not to let it brown.
Sear the Core Vegetables : Add the shaved Brussels sprouts to the skillet, stirring to coat them in the oil. Cook for 5-6 minutes, stirring occasionally, until they become tender and slightly caramelized. Add the grated zucchini, cumin, za'atar, sea salt, and black pepper. Stir continuously for 2 minutes to toast the spices and cook off excess moisture from the zucchini.
Integrate the Creamy Bean Purée : While the vegetables cook, place the rinsed cannellini beans in a small bowl. Using a fork or a potato masher, mash them into a coarse purée. Add the bean purée to the skillet and stir to combine everything into a cohesive, thick base. Cook for 2 minutes.
Wilt the Greens and Form Nests : Add the baby spinach to the skillet in handfuls, stirring it into the hot vegetable mixture until it is just wilted. This should take about 1-2 minutes. Reduce the heat to low. Use the back of a spoon to create three evenly spaced wells, or "nests," in the vegetable base.
Gently Poach the Eggs : Carefully crack one egg into each well. Cover the skillet with a lid and let the eggs cook for 4-6 minutes, or until the whites are set but the yolks are still runny. For firmer yolks, cook for an additional 1-2 minutes.
Garnish and Serve : Remove the skillet from the heat. Immediately sprinkle the fresh lemon zest, chopped cilantro, and dill over the entire dish. Arrange the sliced avocado artfully on top. Serve hot, directly from the skillet.