Melt butter in a 4- to 5-quart saucepan over medium-high heat; add butter, onion, thyme and half of the mace; cook, stirring often, until onions are translucent, about 5 minutes.
Add turnips, potatoes and squash; cook over medium heat, stirring occasionally, until vegetables begin to soften, about 30 minutes. Add broth and TABASCO® Sauce and bring to a boil over high heat. Reduce heat, cover, and simmer until vegetables are very tender, about 30 minutes.
Pour mixture, a portion at a time, into a food processor or blender and process until smooth. Return to pan and heat until steaming. Sprinkle individual servings with remaining mace.
Makes 8 servings.