Cook sausage in a large skillet over medium, stirring to break apart with a wooden spoon, until just beginning to brown, about 6 minutes. Add leek, and cook until sausage is browned and leek begins to soften, about 5 minutes.
Add sausage, chopped leek, and pan drippings to a 6-quart slow cooker. Add stock, collards, garlic, salt, and pepper. Cover and cook on LOW until vegetables are softened and sausage is cooked through, about 4 hours. Stir in cooked pasta and heavy cream just before serving.