Preheat the oven to 400 degrees F. Grease an 8x8 baking dish and set aside.
Heat the butter and olive oil in a large skillet over medium heat. Add the garlic and onion, cook for a few minutes, then add the sliced mushrooms. Cook, stirring occasionally, for 5-7 minutes or until the mushrooms have shrunk down. Add the carrot, peas, and corn and cook for another 5-7 minutes. Season with salt and pepper.
Pour the half and half or milk into the skillet and add the flour. Stir constantly until the mixture starts to thicken. Remove from heat and transfer to the greased baking dish. Top with the shredded cheese. Then add the frozen tater tots in an even layer. You should have just enough to fill an 8x8 baking dish.
Put the hotdish in the oven and cook for 45-60 minutes, or until the cheese starts to bubble and the tater tots are cooked through and slightly browned. Serve warm and enjoy!
I like to add a tablespoon or two of herbs to the veggie mix for more flavor. You can add chopped parsley, sage, thyme, and/or rosemary. Be sure to add salt throughout the cooking process to boost the flavor.
To make this ahead of time, follow all of the steps up until putting it in the oven. Cover tightly and store in the fridge, but only if you are making it the next day. If you are making it at a later time, cover the dish in plastic wrap and then foil and freeze for up to 4 months. You do not need to thaw it in the fridge before baking, since tater tots are cooked from frozen.
Store leftovers in an airtight container in the fridge for 3-5 days.
Reheat leftovers on a plate in the microwave for 2-3 minutes on high. Or you can cover the baking dish with the leftovers with foil and reheat in a preheated oven (300-350 degrees F) for ~30 minutes.