Heat a large nonstick or ceramic saucepan over medium-high heat. Coat with olive oil spray.
Add the chicken, 1/2 teaspoon salt and pepper. Cook, stirring occasionally, until the chicken is cooked through. Using a slotted spoon, transfer to a bowl. Pour out any remaining liquid.
Reduce the heat to medium. Add the olive oil to the saucepan.
Add the onion, celery and carrots. Cook, stirring occasionally, until the onion is translucent, 5 to 7 minutes.
Stir in the garlic, potato, thyme and crushed red pepper. Cook, stirring, for 1 minute.
Pour in the chicken broth and add the bay leaves. Bring the mixture to a boil, then reduce heat so that the broth is simmering. Simmer, stirring occasionally, for 10 minutes.
Remove and discard the bay leaves.
Place the flour in a medium-sized bowl. While whisking, slowly pour in the milk. Whisk well so that the mixture is completely combined.
Stir the milk mixture into the soup. Return to a simmer. Cook, stirring occasionally, until the soup thickens, 12 to 15 minutes.
Remove from the heat and stir in the Cheddar cheese. Once the cheese is melted, stir in the chicken, the remaining 1/4 teaspoon salt and most of the green onions.
Serve, garnishing each bowl with the remaining green onion.