Melt the butter in a Dutch oven over medium heat. Add the onion and cook until softened and translucent, about 5 minutes. Stir in the garlic, cumin, coriander, and nutmeg and cook until the spices are fragrant, about 30 seconds.

Stir in the broth, water, pumpkin, and maple syrup, scraping up any browned bits from the bottom of the pot. Bring the liquid to a boil, then reduce the heat to a simmer and cook for 15 minutes to allow the flavors to meld.

Transfer the soup to a blender in batches and process until completely smooth, about 1 to 2 minutes per batch. Return the pureed soup to a clean pot and stir in the half-and-half. If the soup is too thick, stir in a little more broth until it reaches your desired consistency.

Heat the soup gently over low heat until hot—be careful not to let it boil, which can cause the dairy to separate. Season with salt and pepper to taste and serve warm.