Preheat your oven to 350°F (175°C) to ensure even baking.
In a large mixing bowl, combine the sour cream, Greek yogurt, garlic powder, smoked paprika, cumin, and kosher salt. Stir until smooth.
Gently fold in the rinsed and drained corn and the can of diced green chilies until evenly distributed.
Add the crumbled cotija cheese (or feta) and shredded sharp cheddar cheese to the mixture. Fold gently to combine.
Pour the mixture into a greased baking dish, spreading it out evenly.
Bake for 25-30 minutes, or until the dip is hot and bubbly with lightly browned edges.
Let it cool slightly before serving with tortilla chips, pita bread, or fresh veggies.