Preheat oven to 425 degrees. Lightly grease a 9x13 inch baking dish.
In a large, deep skillet or Dutch oven, melt butter. Add onions and cook until tender, 3-5 minutes. Stir in flour and cook a few minutes more.
Slowly whisk half and half into pan, followed by the chicken broth. Bring to a simmer, whisking constantly, until mixture is thickened. Stir in thyme, onion powder, garlic powder, paprika, and salt and pepper, to taste.
Next, stir in cooked chicken, frozen peas and carrots, and frozen corn. Stir in cheese and cook and stir until cheese is melted.
Pour chicken mixture into prepared baking dish. Arrange frozen tater tots in a single layer on top of the chicken filling.
Bake for 25-30 minutes, or until filling is bubbly and tater tots are golden brown. Let stand for 5-10 minutes before serving. Garnish with fresh parsley, if desired.