In a 3-6 quart crockpot, combine diced potatoes, chicken broth, carrots, celery, onion, salt, garlic, parsley, thyme, and black pepper. Stir well to mix all the ingredients.
Cover the crockpot with the lid and cook on low for 8 hours or on high for 4 hours, until the vegetables are tender.
While the soup cooks, lay the bacon flat on a baking sheet and bake at 350°F for 15-20 minutes until crispy. Let it cool slightly, then chop it into small pieces.
Just before the soup is ready, prepare the roux in the microwave. In a large glass bowl or measuring cup, melt the butter in 30-second intervals until fully melted.
Stir in the flour until well combined, ensuring there are no lumps.
Whisk in the milk until smooth, ensuring all the flour is mixed in. Microwave the mixture in 45-second intervals, whisking each time, until very thick (about 4 intervals worked well for me). Watch closely as it thickens.
Add the thickened milk to the crockpot along with 1 cup of cheese and most of the cooked, chopped bacon, reserving some for topping.
Serve the soup hot, topped with the remaining cheese, bacon, and sliced green onions for a fresh crunch.
Notes
For a vegetarian option, substitute vegetable broth for chicken broth and omit the bacon.