Preheat oven to 375 degrees F.
Add the potatoes to a pot of water. Bring to a boil and let them cook for 15 minutes. (Optional - add Better Than Bouillon and garlic powder to the water)
Drain the potatoes and add them to a mixing bowl. Add up to 1/4 cup of half and half and use a mixer to mash the potatoes.
While the potatoes are boiling, heat a skillet over medium heat. Melt the butter and add the onion. Cook for 3 minutes then add the minced garlic and cook for 1 more minute.
Add the flour to the skillet and give it a good stir. Slowly add in the chicken broth and remaining half and half while stirring, making sure there are no clumps of flour.
Heat the mixture until it simmers, then stir in the chicken and mixed vegetables. If you're not cooking it in an oven safe skillet, transfer the mixture to an 8x8 baking dish.
Top the chicken mixture with small dollops of the mashed potatoes and evenly spread them. Sprinkle the cheddar cheese over the mashed potatoes then bake for 15-20 minutes, or until the cheese is melted.