Heat oil in a medium pan (about 4 quarts) over medium-low heat.
Add the chopped celery, carrot, and onion, and cook, until translucent and tender, but not browned, about 10 minutes. Stir occasionally.
While the vegetables are cooking, peel the potatoes, and rough-cut them into small cubes, ½ to ¾ inch.
Peel, seed and roughly chop the apple.
Add the potatoes, apples, squash, red pepper flakes, and sea salt to the saucepan containing onion mixture.
Stir in the water and the stock and bring to a boil.
Turn the heat to low, cover and simmer the soup until vegetables are tender, 15-20 minutes.
Purée the soup either using an immersion blender (stick blender) or purée in batches in a regular blender. (Be sure to remove the center of the blender cover and hold a towel over the hole while blending, this will allow some of the heat to escape. Otherwise, you run the risk blowing the top off the blender and decorating your ceiling! Yikes!)
Add more water or broth if the soup is too thick.
Serve in bowls and garnish with the crushed amaretti cookies.