Peel the potatoes, and chop them into large 1-inch pieces.
Chop the bell peppers into ½ inch pieces.
Put the potatoes, bell peppers, and oil in a medium pot. Heat on medium low for 3 – 5 minutes. Stir often to prevent the vegetables from sticking to the pot.
Add the spaghetti squash, delicata squash, water, salt, black pepper, and cayenne pepper to the pot. Stir.
Increase the heat to high to bring the water to a boil.
Reduce heat to medium-low to bring it to a simmer. Cook until potatoes and bell peppers are soft, approximately 25 minutes.
Put the basil in a blender.
Transfer the hot soup to the blender. USE CAUTION!
Blend until smooth. Avoid creating a vacuum seal with the blender lid.