Trim, peel, and quarter the turnips, and then chop the turnip greens.
Heat the avocado oil in a medium saucepan over medium heat. Add the turnips and garlic, and cook for 5 minutes or until the turnips are golden on each side.
Add the broth, lemon juice, salt, and pepper, and bring to a boil. Cover and reduce the heat to a simmer. Allow to simmer until the turnips are slightly tender, about 5 to 10 minutes.
Increase the temperature to medium-high heat, add the greens, and cook for another minute or two. Serve warm drizzled with maple syrup and topped with nuts.