Heat oil in a heavy-duty skillet over medium-high heat. Add the onions, peppers and garlic, Sauté until the onions turn light brown (4–5 minutes).
Add the potatoes, salt and pepper and sauté until the potatoes start to brown (5–6 minutes).
Add the turkey, ketchup and broth and fold into the mixture. Cook for 2–3 minutes, scraping the crust that will form on the bottom of the pan (do not burn—the crust adds flavor to the hash). Hold warm.
Poach the eggs.
Portion the hash onto 4 plates (preferably soup plates), then sprinkle with chives and green onions.
Top with the poached egg (sprinkle the egg with chives).