In a 7-8 quart dutch oven, heat the olive oil over medium high heat. Dry the chicken with paper towels and sprinkle with the salt and pepper. When the dutch oven is hot, place the chicken breasts in skin-side down and cook for 5 minutes or until the skin is browned and the chicken releases from the pan.
Flip the chicken and cook an additional 5 minutes, then remove the chicken to a separate plate or shallow bowl. Add the onions, carrots and celery to the dutch oven and cook, stirring occasionally for about 5 minutes, or until the vegetables soften slightly.
Add the diced squash and bay leaf to the pot, and saute, stirring occasionally for an additional 5 minutes. Stir in the white wine and simmer for about 5 minutes, then add in 2 cups of the chicken broth. Add the chicken and any accumulated juices back to the pot.
Bring the stew to a boil. Reduce heat to a simmer, cover and cook for 10-15 minutes or until the chicken is cooked through.
Transfer chicken back to the plate to cool for a few minutes until you can handle it.
Remove the skin and bones from the chicken and shred the chicken meat with your hands, or use a knife to cut it into small chunks. Transfer the chicken back to the pot.
Add the white beans (in their liquid) and escarole to the pot. Stir to combine and heat to a rapid simmer.
Add the cornstarch to the remaining cup of chicken broth and whisk until well combined. Pour the cornstarch mixture into the dutch oven and stir to combine. Bring the stew to a light boil, stirring constantly for one minute. Turn off the heat and cover the dutch oven tightly with a lid. Let the stew rest for 10 minutes, then serve. (The resting time gives the escarole time to wilt and become tender without over cooking it.)