Heat a large cast-iron skillet or heavy-bottomed sauté pan over medium-high heat until very hot (about 3 minutes). Add the olive oil and butter. When the butter foams, add the corn kernels in an even layer. Let the corn sit undisturbed for 2-3 minutes to get a char, then stir and let brown another 2-3 minutes until several kernels are nicely charred. Reduce heat to medium and add the minced garlic and chopped onion; sauté 1-2 minutes until fragrant and the onion is translucent but not browned. Season corn with 1/4 teaspoon salt, 1/4 teaspoon black pepper, smoked paprika, and ground cumin. Remove from heat and set aside.

Prepare cheese base

While the corn cooks, place the cream cheese in a medium microwave-safe bowl and warm for 20-30 seconds until soft (or leave at room temperature until softened). Whisk or beat the soft cream cheese until smooth. Stir in the sour cream, lime juice, and half of the crumbled queso fresco (about 1/2 cup). Fold in the shredded Monterey Jack until combined. Taste and adjust salt (start with the listed 1/2 tsp total salt and add more if needed).

Combine and melt

Return the skillet with the charred corn to low heat (or transfer the corn to a medium saucepan over low). Add the cheese mixture to the pan with corn and gently stir to combine. Heat slowly for 3-5 minutes, stirring frequently, until the cheeses have melted and the mixture is homogenous and warm. Avoid boiling. If the dip seems too thick, stir in 1-2 tablespoons of milk or reserved corn cooking liquid to loosen to desired consistency.

Finish and season

Stir in the remaining crumbled queso fresco and most of the chopped cilantro (reserve a little for garnish). Taste and adjust lime, salt, or spices as needed. Transfer the dip to a warm serving bowl or keep in the skillet on the lowest heat setting.

Serve

Sprinkle the top with chili powder or Tajín and the reserved cilantro. Serve immediately with tortilla chips and lime wedges on the side. For make-ahead: refrigerate cooled dip in an airtight container up to 2 days and rewarm gently on the stovetop or in a 325°F (160°C) oven until hot, stirring and adding a splash of milk if necessary.