Preheat oven to 400 degrees. Coat chicken in vegetable oil, salt and pepper. Bake for 30 minutes. Remove from oven, allow to cool slightly, and shred with 2 forks.
Heat a 12-inch cast-iron skillet over medium heat. Add the butter packets onion, garlic and thyme. Cook until soft, 5 to 7 minutes.
Stir the flour into the onion mixture and cook while stirring for 2 minutes. Stir in the broth, followed by the milk. Add bouillon cube and stir to dissolve. Bring to a boil then turn down to simmer for 10 to 15 minutes, stirring regularly until thick.
Fold in the peas and carrots, pearl onions and shredded chicken.
Cover the pot pie mixture in a circular pattern with tater tots. Place in the oven and bake for 30 minutes, until golden and crispy.