Add carrots, celery, onion, potatoes, broth, and spices to a Crockpot. Cook on high 4-6 hours or low 8-10.
Meanwhile, bake bacon slices on a sheet pan at 400ºF for 20-25 minutes, or to preferred crispiness, and crumble.
For the roux, whisk flour and cornstarch into melted butter until it forms a paste. Whisk in 1 cup half & half until blended well with no lumps, then whisk in remaining half & half. Microwave for 45 seconds.
With a potato masher, mash soup about 8-10 times. Whisk in roux and fold in 1 1/2 cups of the shredded cheese.
Ladle and garnish with additional cheese, green onion, and bacon.