In a large heavy-bottomed pan with a tight-fitting lid, cook sausage over medium-high heat, stirring occasionally, until browned, 4 to 6 minutes; using a slotted spoon, transfer to a paper-towel-lined plate to drain. Set aside.
Add kale to pan in two or three batches, waiting for one batch to wilt before adding the next. Cook over medium until bright green, about 1 minute. Add 1/2 cup water. Reduce heat to medium-low; cover, and simmer until tender, 15 to 20 minutes, stirring once or twice. Uncover; cook until most of the liquid has evaporated. Stir in vinegar; season with salt and pepper. Serve topped with sausage.
I realized after I started making this recipe that didn't have any red wine vinegar so I substituted it with a little lemon juice for the acidity. I doubled the amount of sausage and it was good! It claims it yields 4 servings but it made just enough for 2 of us. It's not a heavy meal, it definitely didn't fill us but it would be a good side to share with a family.