Roughly chop the collards and kale into 1/2-inch pieces. Wash well under cold water. Drain and set aside.
In a large Dutch oven or stockpot over medium heat, add a film of olive oil followed by the turkey wings. Cook until the wings are just about crisped on all sides, about 5 minutes. Add the onions and garlic and a large pinch of salt and sweat until the vegetables are softened and aromatic, about 3 minutes. Add the greens along with the jalapenos, vinegar, sugar and 1 tablespoon salt. Cover and cook until the greens are nicely wilted, 30 minutes. Remove from the heat and check the seasoning, adding salt and vinegar as needed. Add hot sauce to taste and serve.