In a large soup pot over medium-low heat, warm the olive oil. Add onion and saute until soft, about 3 minutes. Add squash, carrots and saute for 10 min. Add the paprika, cumin, turmeric and coriander and continue to saute for 10 min.
Add the stock or water and bring to a boil over high heat. Reduce the heat to low and simmer, uncovered for 30 to 40 minutes, or until the squash and carrots are soft. Remove from heat and let cool slightly.
Working with 2 cups at a time, place soup in a blender and puree on high until smooth and light. As each batch is pureed transfer it to a large saucepan. If using immersion blender, puree soup directly in pot. If soup is too thick, thin with a little water. Should have the consistency of heavy cream.
To serve, place soup over medium-high heat and warm to serving temperature. Season to taste with salt and pepper. In a small bowl whisk the water and the yogurt until smooth. Garnish with a dollop of yogurt, fresh cilantro, chives and fresh lime wedges.