Prepare the vegetables. Rinse and clean the collard greens, kale, turnip greens, and mustard greens. Finely chop the onions and jalapenos.
In a large pot over medium heat, add the olive oil. Once heated, add the turkey wings to the pot and brown on both sides for about 5 minutes.
Add the chopped onions, jalapenos, and a pinch of salt to the pot. Cook for an additional 2 minutes until the vegetables are lightly browned.
Add the collard greens, kale, turnips, and mustard greens to the pot. Stir everything together so that the greens are evenly distributed.
Add 2 cups of water to the pot and bring to a boil. Reduce heat to medium-low and cover the pot with a lid. Simmer for 45 minutes or until the collard greens are tender.
Stir in freshly ground black pepper, taste, and adjust the seasonings to your preference.