Place a sheet pan (with sides) in the oven and preheat to 450.
In a large mixing bowl, toss together the sweet potatoes, olive oil, salt, allspice, cinnamon, smoked paprika, and red chili flakes. Let sit for 5-10 minutes while the oven heats.
Quickly remove the pan from the oven and close the door to prevent heat loss. Pour the sweet potatoes onto the pan, shake to distribute evenly, and quickly add back to the oven. Roast for 25 minutes, shaking the pan every 10 minutes to prevent sticking.
While the potatoes roast, in a sauté pan on medium heat, add olive oil and sage leaves. Fry the sage until the pale green disappears and a little browning develops around the edges. Remove sage from oil and set aside.
Add the turkey sausage to the oil. Let cook for 2 minutes, then toss and add the onions, peppers, thyme, oregano, allspice, smoked paprika, cinnamon, and salt. Sauté for 10 minutes, stirring frequently to prevent burning.
After the sweet potatoes have roasted for 25 minutes, turn on the broiler, setting the pan on one of the bottom two racks. Broil for 3-5 minutes, until dark spots begin to form. Remove from oven.
While the sweet potatoes broil, heat a nonstick pan on medium heat. Add olive oil and all the eggs, sprinkle with salt and red peppercorns (or black if you don't have red). Cover and reduce heat to low, cooking to desired doneness.
Toss together the sweet potatoes and sausage/vegetable mixture. Divide the hash evenly among 4 plates, top each with 2 eggs, and serve warm.