Preheat a cast-iron griddle pan over high heat. Alternatively, prepare a grill for high heat and clean and oil the grates.
Place the corn on the griddle or grill and cook, turning, until charred in spots, about 8 minutes. Transfer to a cutting board. Reduce the heat to low if using a griddle pan or prepare a grill for medium indirect heat: For gas grills (with 3 or more burners), turn off the middle burner and turn the remaining 2 burners down to medium heat.
Meanwhile, whisk the crema, mayonnaise, ancho chile powder, cayenne and 1/4 teaspoon salt in a medium bowl. Put 5 heaping tablespoons of the mixture in a small bowl and set aside.
When the corn is cool enough to handle, cut off the kernels and put in the medium bowl with the remaining sauce. Stir in the Cotija, cilantro, garlic and lime juice.
If using a griddle pan, preheat the oven to 200 degrees F.
Lay the bread slices on a cutting board and spread evenly with the reserved sauce. Flip over 6 slices and top each with 1/4 cup Oaxaca cheese, 1/4 cup of the corn mixture and an additional 1/4 cup Oaxaca cheese. Top with the remaining 6 slices of bread, sauce-side up.
Put 3 sandwiches on the griddle or all 6 sandwiches in the middle of the grill. Press down with a metal spatula and cook until browned, about 3 minutes for the griddle and 2 minutes for the grill. Flip, press down and cook until browned and the cheese melts, about 3 minutes for the griddle and 2 minutes for the grill. If using a griddle pan, transfer to a rimmed baking sheet and keep warm in the oven. Repeat with the remaining 3 sandwiches. Slice each sandwich in half and serve.