Preheat your oven to 375°F (190°C). Grease a 9x13 inch baking dish with a bit of olive oil or butter.
In a large skillet, heat the olive oil over medium heat. Add the diced sweet potatoes and sauté until they start to soften, about 10 minutes. I've found that covering the skillet with a lid helps them cook faster and more evenly.
Add the minced garlic and cook for another minute until fragrant. It's crucial not to let the garlic burn, as it can introduce a bitter taste.
Stir in the spinach and cook until just wilted. This usually takes about 2 minutes. The spinach should retain its vibrant green color, signaling it's perfectly cooked.
Transfer the sweet potato and spinach mixture to the prepared baking dish, spreading it out evenly.
In a mixing bowl, whisk together the eggs, milk, smoked paprika, dried thyme, salt, and pepper. When I first made this recipe, I whisked the eggs only lightly, but I've since learned that a vigorous whisk incorporates more air and results in a fluffier casserole.
Pour the egg mixture over the sweet potatoes and spinach in the baking dish. Let it sit for a moment to allow the eggs to seep into the nooks and crannies.
Sprinkle the shredded cheddar cheese evenly over the top. Then scatter the sliced green onions on top of the cheese. I've tried various cheeses, but sharp cheddar consistently delivers the best flavor punch.
Bake in the preheated oven for 25 to 30 minutes, or until the eggs are set and the top is golden brown. A dear friend, who's a chef, once suggested placing the casserole under the broiler for the last 2 minutes for an extra-crispy top, and it's been my go-to ever since.
Remove from the oven and let it cool for 5 minutes before slicing. This rest period allows the casserole to set, making it easier to cut into neat portions.