Heat oil in a large, nonstick pot or cast iron Dutch oven.
Add onion and jalapeno and saute until onions are translucent.
Add corn kernels and seasonings. Cook over medium-high heat for 8-10 minutes, stirring frequently.
Add garlic and cook until fragrant.
Remove 1-½ cups of corn mixture from the pot and set aside.
Stir in broth, milk, and cheese and simmer for 20 minutes.
Transfer soup to a blender or food processor to puree until smooth.
Return soup to pot and gently reheat to desired serving temperature if needed.
Stir in half (¾ cup) of the reserved corn mixture, lime juice, and 2 tablespoons chopped cilantro.
Season to taste with salt and pepper.
Use the remaining corn as a garnish with cilantro and additional cheese.