In a large iron skillet, heat vegetable oil over high heat until shimmering.

Add corn. Let sit without stirring for two minutes, until corn begins to char. Stir once and let sit for another two minutes.

Add shrimp. Continue to cook, stirring once every two minutes, until shrimp is cooked through, corn has blackened bits and is beginning to pop in the pan. You want a dry pan for the corn to blacken properly-- if the shrimp or corn release too much water during cooking, you can drain it off with a strainer and return the corn and shrimp to the skillet to continue charring. I find this is usually only a problem with frozen shrimp.

Put corn and shrimp in a large heatproof bowl, scraping the skillet as you go so you don't lose any of those delicious blackened bits. Add in the tomatoes, shallots, jalapeño, basil, mayonnaise, Cojita cheese, lime juice, chili powder and paprika. Taste and add salt, additional lime juice, chili powder, mayo or paprika as needed.

Serve with a slotted spoon into four bowls or plates. Top with green onions, additional Cojita cheese and, if desired, a sprinkle of chili powder or paprika.