Preheat oven to 425°F (220°C).
Place poblano peppers on a baking sheet and roast until charred (about 20 minutes), turning occasionally.
Transfer peppers to a bowl, cover with plastic wrap, and let steam for 10 minutes. Peel skin, remove seeds, and dice.
Heat olive oil in a skillet over medium heat. Add onion, garlic, and corn; sauté until softened (5 minutes).
Stir in cumin and smoked paprika; cook for 1 more minute.
In a mixing bowl, combine cream cheese, sour cream, roasted poblanos, sautéed corn mixture, lime juice, cilantro, salt, and pepper.
Fold in 1 cup Monterey Jack and all cheddar cheese.
Transfer to a baking dish, sprinkle with remaining Monterey Jack, and bake for 15 minutes until bubbly and golden.
Serve hot with tortilla chips, bread, or veggies.