Preheat the oven to 350°.
In a large skillet over medium heat, melt the butter with the olive oil. Add the leeks and cook, stirring occasionally, until they are soft and tender but not browned, 6 to 8 minutes. Add the garlic and spinach, season with salt, and cook until the spinach has wilted, 2 to 3minutes.
Set 2 small ovenproof dishes onto a baking sheet. Divide the spinach-leek mixture equally between the dishes. Make 2indentations in each dish, leaving about a 1-inch gap in between. Carefully crack each egg into an indentation. Pour 2 tablespoons of cream into each dish and season with salt.
Place the baking sheet into the oven and bake until the whites are just set but the yolks are still runny, 10 to 12 minutes.
Top the baked eggs with the thyme, lemon zest and Aleppo pepper, and serve.