Place the chicken breasts in a stockpot or Dutch oven and add enough cold water to cover. Sprinkle with a pinch of salt and add a bay leaf. Bring the pot to a boil, reduce the heat, cover, and let the chicken simmer for 15-20 minutes or until cooked through and no longer pink inside.
Remove the chicken from the pot and let it cool. Shred it and set it aside. Rinse and dry the stockpot.
In the same stockpot, heat the oil over medium-high heat. Sauté the onions in the oil for about five minutes until soft. Add flour and cook for two more minutes, stirring often. Add broth, stir well, and boil to thicken slightly.
Add the squash and potatoes and return the soup to a boil.
Reduce heat, and let simmer 20 minutes or until vegetables are tender.
Remove soup from the stove and puree with an immersion blender. Alternatively, place most of the solids along with a cup of the liquid in a regular blender and blend until smooth. Pour the pureed portion back into the pot and stir well.
Return creamed soup to the stove, and add corn, chicken, and thyme.
Simmer for 10 minutes or until corn is tender.
Add red peppers and scallions, and continue to simmer for 5 minutes or until the peppers are slightly softened but still firm.
Finally, add cilantro and cream and heat through.
Season with about 1.5 teaspoons of salt (or to taste).