Preheat oven to 400°. Put all vegetables (including garlic) except sweet potatoes into a very large bowl (or two large ones); put sweet potatoes in a separate bowl. Drizzle bowls generously with olive oil and sprinkle with salt and pepper. Toss gently with your hands to coat; then spread half of mixed vegetables on two large baking sheets. Break up 3 rosemary sprigs and sprinkle over vegetables.
Roast vegetables 15 minutes. Stir gently with a metal spatula if they are sticking. Add half of the sweet potatoes to pans. Continue roasting, stirring vegetables every 15 minutes if necessary and changing positions of pans to ensure even browning, until vegetables are browned and tender, 40 minutes to 1 1/4 hours. Remove from oven and set aside. Repeat with remaining half of mixed vegetables, sweet potatoes, and 2 1/2 rosemary sprigs.
Pour vegetables onto a serving platter and season to taste with salt and pepper. Garnish with remaining sprig of rosemary and serve warm or at room temperature.
Note: Nutritional analysis is per serving.