Turn the Instant Pot to "sauté" mode on high temperature for 5 minutes. Push the start button and add the butter, shallots, celery, sage and 1/4 teaspoon salt. Stir occasionally.
Turn the Instant Pot to “pressure cook” mode on high temperature for 5 minutes. Push the start button and then add one cup of broth, vermouth, apple, squash and remaining salt. Stir well and lock on the lid.
Immediately do a "quick release" and remove the lid when the pin drops. Add the remaining one cup of broth, vinegar and pepper. Blend with a blender or an immersion blender until thick and creamy, about 1 minute. Taste to assess the seasoning and the thickness. Add more salt and/or broth, as needed. Keep warm.
Make the fried sage. In a small sauté pan on medium heat, melt the butter.
Fry the sage leaves in the butter. Cook until the butter is brown and the leaves are crispy, about 1 minute.
Ladle the soup into individual bowls, then top each one with several drops of brown butter and a few crispy sage leaves. Enjoy!