Preheat the oven to 400°F.
In a large skillet over medium heat, combine the olive oil and garlic. Sauté for 3 minutes.
Add the tomato paste, oregano, garlic powder, thyme, cinnamon, smoked paprika, chili powder, nutmeg, and salt. Stir and cook for 2 minutes longer.
Add the vegetable broth, lemon juice, and jack-fruit. Stir and then let simmer for 10 minutes.
When the jackfruit is done simmering, transfer to a baking sheet. Using the back of a fork, break the jackfruit up a bit into shreds. Bake for 15 minutes.
Divide the jackfruit among the pitas or flatbread. Top with lettuce, tomato, red onion, and a dollop of tzatziki before serving.