1. Melt 1 tablespoon butter with oil in a large heavy skillet over medium heat. Add kale; reduce heat to low. Cook until soft.
2. Add spinach and season with salt. Increase heat to medium-high. Cook, turning frequently until wilted (4–5 minutes).
3. Transfer spinach mixture to 10" skillet, leaving any excess liquid behind. Make 2-4 indentations and carefully break 1 egg into each hollow, taking care to keep yolks intact. Bake until egg whites are set (10–15 minutes).