Heat oil in a 12" skillet over medium-high. Crush cumin, coriander, and red pepper with a mortar and pestle or heavy skillet. Add to hot oil in skillet and stir to coat. Add onions and mushrooms and cook, stirring often, until softened and lightly browned, 6–8 minutes. Add tomatoes, vinegar, and 1 tsp. kosher salt and stir to combine. Add kale, cover skillet, and cook, uncovering and tossing occasionally, until kale is wilted, 4–6 minutes. Season with remaining 1/2 tsp. kosher salt.
Make 8 indentations in vegetable mixture. Carefully crack an egg into each. Cover skillet and cook over medium-low heat, rotating skillet on burner halfway through to ensure even cooking, until egg whites are opaque and just set, 8–10 minutes. Top with sea salt, herbs, and Aleppo-style pepper (if using). Squeeze lemon juice over.