Golden Harvest Potato Bake

I tried this at Thanksgiving and really loved it. The carrot flavor really shines through, so next time I make it I might only add three carrots.

5 pounds Yukon Gold potatoes, peeled and cubed
2 medium sweet potatoes, peeled and cubed
5 large carrots, cut into 2-inch pieces
3 garlic cloves, minced
1 tsp dried tarragon (we didn't have any so I didn't use it)
1 cup shredded cheddar cheese, (divided)
1/2 cup milk
2 eggs
2 TB cider vinegar
1 TB butter
1 tsp salt
1 tsp dried parsley flakes
1/2 to 1 tsp of pepper

Place the potatoes, carrots, garlic and tarragon in a Dutch oven (I just did it on the stove top) cover with water. Bring to boil. Reduce heat; cover and cook for 15-20 min or until tender. Drain.
In a large bowl, mash vegetables. Stir in 1/2 cup of cheese, milk, eggs, vinegar, butter, salt, parsley and pepper until blended.
Transfer to a greased 13x9 in baking dish; sprinkle with the remaining cheese. Bake uncovered, at 325 degrees for 25-30 min.