For the sauteed onions and mushrooms: Heat 2 tablespoons of the olive oil in a large skillet over medium heat. Add the onions and saute until softened and translucent, 3 to 4 minutes. Add the mushrooms and remaining 2 tablespoons olive oil and season generously with salt and pepper. Add the coriander and cumin and stir. Saute until the onions and mushrooms have cooked down and are lightly browned, about 8 minutes, making sure to stir every minute. Keep warm until ready to serve on top of the burgers.
For the grilled corn: Preheat a grill to medium heat.
Brush each ear of corn with the olive oil. Sprinkle each with some of the ground cumin and salt. Grill until the kernels are softened and slightly charred, 10 to 12 minutes, turning a quarter turn ever 3 minutes.
For the burgers: In a medium bowl, mix the Cheddar and mozzarella together. In a large bowl, combine the beef, lamb, pork, veal, coriander, cumin, salt, pepper and 3/4 cup of the cheese mixture. Mix until everything is thoroughly combined. Form into 4 even patties. Place on a plate.
Preheat a grill or grill pan to medium-high heat.
Brush the grill grates with canola oil. Place the burgers on the grill and cook until browned and grill marked, 3 to 4 minutes. Flip the burgers, cover and cook another 2 minutes. Top each burger with a generous amount of the remaining cheese mixture, cover and let cook until the cheese is melted, about 2 minutes.
Place the burgers on the buns and top with the sauteed onions and mushrooms. Let guests top with their choice of condiments, such as ketchup, mustard, mayonnaise, lettuce, tomato slices, onions or pickles. Serve with the grilled corn on the side.