Preheat oven to 375 F.
Peel and chop the russet potato and sweet potato into 1-inch cubes and steam until tender. Place the cooked potatoes in a large mixing bowl and set aside.
Dice the onion, peel and chop the carrots, then add both to a large, deep-sided pan with a splash of olive oil. Saute the carrots and onion until just beginning to soften.
Add the beef and dried thyme, breaking up the meat with a spoon. Turn the heat up to medium-high, and continue to cook, stirring often, until the beef is no longer pink.
Sprinkle the beef, carrot, and onion mixture with flour. Stir the mixture to incorporate the flour, then add 1/2 cup water and cook another 5 minutes, stirring often. (A roux will form around the meat.)
Remove from heat and stir in frozen peas, corn, and Worcester sauce.
Press the filling into a 9 x 9 baking dish.
To the mixing bowl of potatoes, add the half-and-half, 2 tablespoons olive oil, and salt and pepper to taste.
Use a potato masher (or a big fork) to mash it all up until it becomes smooth and creamy.
Spread the topping over the filling in the baking dish, and bake at 375 for 20 minutes or until heated through.
Garnish with a sprinkle of chives, and serve.