In a deep 12-inch skillet or large saucepan over medium heat, cook bacon until crisp. Transfer to paper towels to drain, then crumble. Drain fat from skillet.
Add oil and heat over medium heat. Add onion, celery and carrots and sauté until softened, about 10 minutes. Add potatoes, salt, pepper and stock and bring to boil. Reduce heat and simmer, covered, until tender, about 15 minutes.
Add milk and corn and simmer, covered, 5 minutes. Stir in jalapeños and cheese until cheese is melted. Garnish each serving of peppery corn soup with cilantro and bacon.