Peel the russet potatoes and cut 1 in half and set it aside with the sweet potato. Roughly chop the remaining potatoes into a 1/2-inch dice. Place in a saucepan and cover with cold water and a few shakes of salt, then set over high heat and bring to a boil for 10 to 15 minutes.

When the potatoes are fork-tender, drain them through a colander set inside a bowl, then return to the saucepan. Mash the potatoes with a few splashes of the potato water, then add the butter, milk, 1 teaspoon salt, and 1/2 teaspoon black pepper; continue to mash until smooth. Season with more salt and pepper to taste.

Preheat the oven to 375 degrees F.

While the potatoes are cooking, prepare the filling. Heat the oil in large saute pan set over medium-high heat. Add the onion and saute until they begin to soften, 3-4 minutes. Add the garlic and stir to combine.

Add the beef and chopped mushrooms and cook until browned and cooked through, 3-5 minutes. Sprinkle on the flour and stir to coat. Cook for 1 minute.

Splash in the wine and deglaze the pan. Add the broth, tomato paste, Worcestershire, and herbs, and stir to combine. Season with remaining salt and pepper. Bring mixture to a boil, then reduce the heat to low, cover and simmer 10-12 minutes until the sauce has thickened slightly.

Remove the pan from the heat and add the mixed vegetables, stirring to combine. Spread the mixture evenly into a 2-quart casserole dish. Top with the mashed potatoes, starting around the edges to create a seal to prevent bubbling.

Use a mandoline to cut the half russet potato and sweet potato into thin slices. Place each potato variety in a microwave-safe container with 1/4 cup of water; cover. Microwave for 4 minutes, then carefully drain the slices through a colander. Rinse with cold water, then place the slices in a bowl of cold water.

Shingle the potato slices on top of the mash, overlapping the slices in alternating layers. Brush with the melted butter, then sprinkle on a bit of black pepper. 

Place on the middle rack of the oven and bake for 25 minutes or just until the potatoes begin to brown. Sprinkle the cheese on top (if using) and broil for 3-4 minutes until browned. Remove from the oven and cool for at least 15 minutes before serving. Garnish with fresh thyme.