In a large bowl, toss the cubed sweet potatoes with olive oil, salt, and pepper. Spread them evenly on a baking sheet and roast for about 20-25 minutes, or until tender and lightly caramelized. Set aside to cool slightly.
In a large mixing bowl, whisk together the eggs, milk, garlic powder, onion powder, thyme, and smoked paprika until well combined. Season with salt and pepper to taste.
In a large greased baking dish, layer half of the cubed bread, followed by half of the roasted sweet potatoes, half of the ground turkey, half of the spinach or kale (if using), and half of the cheese. Repeat the layers with the remaining bread, sweet potatoes, turkey, spinach, and top with remaining cheese.
Slowly pour the egg mixture over the layered strata, ensuring the bread is evenly soaked. Use a spatula to gently press down the layers to help the bread absorb the liquid. Allow it to sit for about 10-15 minutes.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes. Remove the foil and bake for an additional 15-20 minutes, or until the strata is set in the center and the top is golden brown and bubbly.
Allow the strata to cool for about 10 minutes before slicing. Garnish with fresh herbs if desired, and serve warm.