Place the chicken stock, onion, carrot, celery, bell pepper, butter, salt, black pepper, and crushed red pepper in a 6-quart or larger slow cooker. Cover and cook on HIGH until vegetables are tender, about 3 hours.
Using a hand blender/kitchen emulsifier or blender, pulse the mixture to break up the tender vegetables. If using a blender, use a ladle to spoon the vegetables into the blender with a bit of liquid. This way, the majority is processed, however they may still be some larger pieces which is fine.
Whisk Cheddar cheese with 1 tablespoon of the cornstarch. Cream the cream cheese and 1 cup of the milk. At the same time, add both the cheese and the cream cheese milk mixture in to the slow cooker. Whisk to combine. Cover and cook on HIGH until cheese is melted and smooth, whisking occasionally, about 30 minutes.
Whisk together the remaining cornstarch and remaining ¼ cup milk in a small bowl until smooth. Whisk into soup in the slow cooker. Cover and cook on HIGH, whisking occasionally, until thickened, about 15 minutes.
Portion into serving bowls or serve in bread bowls. Garnish with croutons, bacon, scallions, or a combination.