Preheat the oven to 425°F.
In a medium saucepan, melt the butter over medium heat. Add the diced onions and saute until onion is translucent, about 3 to 4 minutes.
Add the flour, salt, and pepper. Cook, stirring constantly until the flour mixture begins to brown, about 3 to 4 minutes.
Slowly stir or whisk the chicken broth and whole milk into the flour mixture. Stir constantly while pouring just a bit at a time to make a smooth mixture.
Continue cooking over medium heat, stirring constantly to ensure that the milk does not burn on the bottom of the pan, cook until mixture begins to bubble and thicken slightly about 5 minutes. Remove from heat.
Stir in the cream cheese, frozen vegetables, and diced chicken. Stir to mix evenly.
Spread the pot pie mixture into a 9x13 baking dish. Spread the tater tots evenly over the top.
Bake approximately 40 minutes or until the tater tots are golden brown and the casserole is bubbly.
Top with cheese and return to the oven for 3 to 5 additional minutes until the cheese is melted.