Heat the oil and bacon in a medium soup pot. When it starts to sizzle, add the onion, carrot, celery, and garlic.
Add the corn and saute another couple of minutes.
Add the broth, water, potatoes, and corncobs. Cook until the potato is cooked through, about 5-10 minutes
Add the smoked paprika and the milk mixed with the flour. Cook another 5 minutes. Remove the corncobs.
Using a hand blender, puree about half the soup or put half the soup in a blender and puree.
Heat through, then turn the stove off and stir in the cheddar cheese. Taste and add salt and pepper (it will need several large pinches of salt). If you like grill seasoning or any other flavored pepper you can use that.