In a 4 quart Dutch oven or heavy bottom soup pot, add the oil and heat on medium until it shimmers.
Add the onion and saute on medium low for 7-8 minutes or until just softened.
To the soup pot, stir in the corn, jalapeños, garlic, paprika, salt and potatoes. Pour in the broth and water. Stir. Bring to a simmer and cook on a low simmer for about 13-18 minutes, or until the potatoes are just fork tender, stirring occasionally to prevent any sticking.
Transfer about 1 1/2 cups of the soup mixture to a blender and pour in the milk. Blend until smooth, about 30 seconds. Transfer the blended soup back into the soup pot and stir in the beans. Cook on low for about 5 minutes just to warm through.
Remove from heat, stir in the cheese and squeeze in the juice of half a lime. Taste for salt adjustment.
Ladle into soup bowls, add a few twists of fresh ground black pepper and garnish as desired.