Preheat oven to 375°. Cut top third off each squash. Scoop out seeds from squash bottoms and tops; discard. Trim just enough off bottom of each squash so that it sits straight.
Set squash bottoms and tops on 2 large baking sheets and drizzle with about 2 tbsp. oil, rubbing it all over insides and rims. Bake 45 to 55 minutes, or until the flesh is soft and golden brown, but before squash start collapsing.
Meanwhile, heat remaining 2 tbsp. oil in a large pot over medium heat; add onion, paprika, sage, and 1/2 tsp. salt and cook until golden brown, about 5 minutes. Add garlic and cook 2 minutes more.
Scoop cooked flesh from squash into pot, leaving enough flesh so that squash keep their shape. Pave over any holes in squash "bowls" with some cooked squash and keep them warm.
To pot add 5 cups stock, remaining 1 tsp. salt, and the pepper. Bring to a boil; reduce heat and simmer 5 minutes. Add salt to taste.
Purée soup in batches in a blender, adding more stock if soup is too thick (cover top with a towel to keep hot soup from spurting out). Reheat in pot. Stir in crème fraîche and more stock if necessary.
Ladle soup into squash bowls and top with sage leaves.
Note: Nutritional analysis is per serving.