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. Cook until the spices are fragrant, about 30 seconds—keep them moving so they do not scorch.

Stir in the broth, water, pumpkin, and maple syrup, scraping the bottom of the pot to release any browned bits. Bring the mixture to a boil, then reduce the heat to maintain a gentle simmer for 15 minutes to let the flavors meld.

Working in batches, process the soup in a blender until completely smooth, about 2 minutes. Fill the blender jar only halfway and hold the lid down firmly with a folded towel to vent steam safely.

Return the pureed soup to a clean pot and stir in the half-and-half. If the texture is too thick, stir in additional broth a splash at a time until the soup is velvety.

Heat the soup gently over low heat until steaming, but do not allow it to boil or the dairy may break. Season with salt and pepper to taste and serve warm.