Preheat the oven to 400 degrees Fahrenheit.

Peel the potatoes and cut them into large chunks. Add them to a large pot and cover them with enough water until they are just submerged.

Bring the potatoes to a boil on the stovetop over medium/high heat. Reduce the heat to medium, cover the pot with a lid, and boil the potatoes for 10-15 minutes or until they are fork-tender.

While the potatoes are boiling, melt 4 tablespoons of butter in a large skillet on the stovetop over medium/high heat. Add the onions and garlic to the skillet and sauté for about 3 minutes.

Add the flour to the skillet, and stir to combine,

Add the chicken broth, 1 cup milk, salt, pepper, and thyme to the skillet and whisk briskly until the mixture is smooth and thickened.

Add the frozen vegetables and cooked chicken to the sauce and stir to combine. Allow the mixture to simmer on LOW heat while you prepare the mashed potatoes.

Drain the water from the pot of potatoes and add the remaining 4 tablespoons of butter, remaining milk, and sour cream to the pot and mash the potatoes with a potato masher until fluffy. Season with salt and pepper to taste and stir to combine.

Pour the chicken mixture into a 9x13-inch casserole dish.

Spread the mashed potatoes evenly over the top of the chicken mixture.

Bake the shepherd's pie in the preheated oven for 30 minutes or until the edges are bubbling and the top is lightly golden brown.