In a heavy-bottomed pot over medium-high heat, add 2 turns of the pan of EVOO. Cook ground turkey until brown, about 5 minutes. Add in the onions, garlic and peppers, and cook until onions are translucent, about 5-6 minutes. Stir in chili powder, cumin, cinnamon, allspice, tomato paste, salt and ground black pepper, and cook about 1 minute. Add in the beer, chicken stock and honey and bring up to a bubble. Simmer for about 15 minutes.
While the chili is cooking, heat a high-sided saut pan over medium heat with half an inch of oil. The oil is ready when rapid bubbles form around the bottom of a wooden utensil handle when it is inserted into the oil. When properly heated, carefully add the okra into the oil and fry until crispy and tender, about 2-3 minutes. Remove with a slotted spoon to a paper towel-lined plate and sprinkle with salt.
Just before serving, add the lime zest and juice to the chili. Spoon chili into bowls and top each portion with some fried okra.