In a 4- to 5-quart saucepan or Dutch oven, heat the butter over medium-low heat. When hot, add the shallots, leeks, celery, garlic, and a pinch of kosher salt. Stir well, cover, reduce the heat to low, and cook, stirring occasionally, until the aromatics are softened, 8 to 10 minutes. Stir in 1 tsp. kosher salt and the garam masala.
Add the butternut squash, vegetable broth, and cider, stir well, and bring to a simmer over medium heat. Cook, uncovered, stirring occasionally, until the vegetables are very tender and the soup is full-flavored, 7 to 20 minutes.
Take the pan off the heat and let the soup cool for 5 minutes. Working in batches, puree the soup in a blender (fill the jar no more than half full and vent the lid, topping it with a folded kitchen towel to prevent hot splashes). Wipe the pan clean and put the soup back into the pan.
Add the yogurt and 1/2 tsp. of the lime juice. Season the soup with salt and pepper. Taste the soup and adjust the seasonings with more salt, pepper, or lime juice as needed.
Ladle into 8 soup bowls and garnish each serving with 1 to 2 tsp. chopped cilantro.