To make the corn strips, cut the tortillas in half and then into thin strips, about 1/2" wide.. Heat 1 cup of vegetable oil in a skillet over medium-high heat. In batches, fry the tortilla strips for 1-2 minutes, or until browned and crispy, flipping them about halfway through. Set them on paper towels to cool.
Whisk the eggs and the heavy cream together in a large bowl. Season to taste with salt and pepper. Set aside.
Remove the oil from the pan used for frying the tortilla strips. Add the remaining 1/4 cup oil and heat over medium heat. Saute the mushrooms for about 3 minutes. Add the leeks and cook for another couple of minutes. Add the garlic and saute for 1 minute.
Pour in the egg mixture and cook, stirring constantly, in a circular motion until the eggs begin to solidify. Stir in the fried tortilla strips. Continue cooking and stirring until eggs are cooked through.
Remove from heat, top with cheese. Serve right away.