In a large saucepan over medium heat, heat oil until shimmery. Add kale stems and garlic. Cook, stirring often, for about 1 minute, until softened. Stir in salt and pepper. Add kale leaves. Cook, stirring often, for 1 to 2 minutes, until coated and slightly wilted. Pour in stock. Cover, reduce heat to medium low and cook, stirring occasionally, for about 10 minutes, until kale is tender-crisp and stock has evaporated. Drizzle with vinegar to taste. Serve warm.