Preheat your oven to 350°F and lightly coat a 9 x 13 x 2-inch baking dish with nonstick cooking spray. In a large skillet over medium-high heat, cook the ground beef until it is fully browned and no pink remains, breaking it apart as it cooks. Season with salt and black pepper, stirring to combine. Add the diced onion and both red and green bell peppers to the skillet, cooking for a few minutes until the onion becomes soft and translucent. Drain any excess grease from the skillet and turn off the heat.

While the meat cooks, peel the russet potatoes and slice them thinly. Place the sliced potatoes in a large bowl filled with cold water to prevent browning and remove excess starch. In a separate medium bowl, whisk together the evaporated milk, cream of mushroom soup, and cream of chicken soup until smooth and well blended.

Drain the sliced potatoes and pat them dry using clean paper towels. Arrange half of the potato slices evenly in the bottom of the prepared baking dish. Spoon half of the beef and vegetable mixture over the potatoes, then pour on half of the soup mixture, followed by 1½ cups of shredded cheddar cheese. Repeat these layers with the remaining potatoes, meat, sauce, and top with the remaining 1½ cups of cheese.

Sprinkle the fried onions evenly over the top of the casserole, then cover the dish tightly with aluminum foil. Bake in the preheated oven for 75 to 80 minutes, or until the potatoes are fork-tender and the internal temperature has reached 165°F. Remove the foil and place the casserole under the broiler on high for 1 to 2 minutes, just until the top is golden and slightly crisp.

Allow the casserole to rest for about 10 minutes before serving, giving the potatoes time to absorb any remaining liquid and the layers to set.