Lighter Sheperd's Pie (Can be made vegan)

I know it's not St. Patrick's Day, but good food is good food!  This is the kind of food that is great for the fall it's also not hard to make.  To make this you will need:
For the potatoes: *
1 1/2 pounds yams
1/4 cup fat free half-and-half (Soy Creamer)
2 ounces unsalted butter
3/4 teaspoon kosher salt
1/4 teaspoon freshly ground black pepper
1/4 cup egg beaters (Skip this totally)
For the meat filling:
2 tablespoons canola oil
1 cup chopped onion
2 cups chopped carrots
2 cloves garlic, minced
1 package ground turkey (Soy crumbles)
1 teaspoon kosher salt
1/2 teaspoon freshly ground black pepper
2 tablespoons all-purpose flour
2 teaspoons tomato paste
2 cups chicken broth (vegetable broth)
1 tablespoon Worcestershire sauce (use vegan brand)
2 teaspoons freshly chopped rosemary leaves
1 teaspoon freshly chopped thyme leaves
8 ounces mushrooms, rough chopped
1 cup frozen peas

1.)  Peel the potatoes, cut them into 1 inch pieces put into a medium saucepan and fill with cold water.  Bring to a boil over high heat.  Once they start to boil, reduce the heat and simmer until the potatoes are fork tender.  Approximately 20 minutes.  Drain, return to pan, add the remaining ingredients and mash the potatoes.  Put aside.
2.)  Heat oven to 400 degrees.
3.)  In a large fry pan over medium high heat, add the canola oil.  Add the onions and the carrots.  Saute for 4 minutes.  Add the garlic and stir to combine.  Add the ground turkey, salt and pepper breaking up the turkey.  Cook until the turkey has browned.  Sprinkle with the flour and stir to combine.  Add the tomato paste, the chicken broth, the rosemary, the thyme and the mushrooms.
Stir to combine.  Let this mixture cook for about 10-12 minutes.  Until the sauce is thickened.
4.)  Stir in the peas.  Spray a casserole dish with Pam and pour in the meat filling.  Top with the mashed potatoes.
5.)  If your casserole dish is very full, bake the casserole with a baking sheet underneath for any overflow.  Bake in the oven for 25 minutes.  It will be very hot so allow it to cool for 10 minutes before digging in!

*In a hurry, buy the prepared sweet potatoes at the market!
To adapt this to vegan, substitute the items in the brackets.