Heat 1 Tbsp. oil in large pot over medium heat. Add onion and sauté 2–3 minutes until softened. Add garlic and sauté another 1–2 minutes.
Add ground turkey and a pinch of salt and pepper to the pot with onions and garlic. Cook, breaking apart with a spoon or spatula, until cooked through (about 5–8 minutes). If using leftover turkey, add during step four along with the hominy.
Add tomato paste and chipotle pepper. Cook 2–3 minutes, breaking chipotle pepper apart with the spoon. Add broth and hominy; stir until incorporated. Simmer for 10–15 minutes until flavors have incorporated.
Remove soup from heat, add green onions and stir to combine.
Divide the sliced cabbage among four bowls. Spoon the pozole over cabbage and top with radish slices, fresh cilantro and a fresh squeeze of lime. For added creaminess and texture, top with a dollop of Greek yogurt and serve with tortilla chips.