Add celery, carrots, onion, and squash to a large saucepan/soup pot. Saute, stirring frequently, in 3 Tbsp olive oil, adding more oil if needed to prevent pot from becoming dry. Stir in 1/4 teaspoon salt and 1/4 teaspoon pepper.
After about 5 minutes (once veggies have begun to soften), stir in potatoes and an additional 2 Tbsp olive oil. Cook, stirring frequently, for about 10 minutes (until you can easily mash the potatoes and veggies with a wooden spoon).
Add broth, and bring to a healthy boil. Cook, stirring frequently, for 15 minutes.
Meanwhile, cook your bacon in the microwave, until slightly crunchy but not burnt. Remove, and allow to cool for a few minutes before chopping. Save 1 Tbsp bacon grease, and add it to the pot of soup. It's optional, but it adds flavor.
In a small saucepan, whisk together milk and heavy cream over low/medium heat. Slowly add flour, whisking constantly until mixture starts to thicken and bubble. Remove from heat. Quickly whisk in sour cream, and stir mixture into soup.
Stir in cheese and 1/2 cup green onions.
Turn down burner heat to low, and use an immersion blender/Bamix to remove lumps from soup. You can also use a regular blender, if your blender is rated for hot liquids. When using an immersion blender, make sure the blade is fully immersed before turning it on, and make sure the device is completely turned off before removing it from the soup. This prevents hot liquid from flying everywhere.
Remove soup from heat, and stir in the majority of bacon slices. Add additional salt and pepper to taste. Serve in bowls, garnished with remaining green onion and bacon.
Recipe makes approximately 3 quarts of soup