Begin cooking by preheating the oven at 400°F or 200°C.
Take the pumpkin, peel its skin, and dice it into cubes using a knife. Repeat the same process with the rutabaga. Peel the skin of the shallots and cut them into wedges. For the garlic cloves, simply peel them.
Spread all the veggies on a baking sheet, sprinkle olive oil, salt and pepper, and roast them in the oven for 25-30 mins. Instead of baking, you can also fry the veggies over medium heat. Keep frying until pumpkin and turnip are soft and mushy.
From the baking sheet or pan take the roasted veggies and put them in a pot with vegetable stock or water. Bring the mixture to a boil and after letting it simmer for a few minutes take it off from the stove.
Pour small cubes of butter into the broth and using a hand blender, whisk it to a smooth texture. Finish it by adding lime juice, herbs, and salt and pepper.