Heat a small amount of extra-virgin olive oil in a stainless-steel skillet over medium-low heat. Add the lean ground beef and gluten-free Italian sausage, separating the meat into small pieces with a spatula. Cook until both meats are evenly browned.
Add the diced sweet onion and minced garlic to the skillet. Continue cooking until the onion becomes soft and translucent.
Stir in the frozen mixed vegetables and cook for approximately 4 minutes, allowing them to begin softening.
Move the meat and vegetables toward the edges of the skillet to create an open space in the center. Spoon the tomato paste into this area and cook it for about 1 minute to deepen its flavor.
Combine the toasted tomato paste with the meat mixture. Season with dried thyme, salt, and black pepper, then add the gluten-free Worcestershire sauce and broth.
Bring the filling to a gentle simmer. Reduce the heat and cook uncovered for 30 minutes, or until most of the liquid has evaporated and the mixture has developed a thick consistency. Taste and adjust the salt, pepper, or thyme as needed.
While the filling simmers, preheat the oven to 400°F (200°C).
Using a mandoline or a sharp knife, cut the russet potato and peeled sweet potato into thin, even slices. When the slices are especially moist or begin sticking together, coat them very lightly with rice flour to help keep them separate.
Lightly grease a pie dish with olive oil or nonstick cooking spray. Transfer the hot beef and vegetable filling into the prepared dish and spread it into an even layer.
Arrange half of the russet and sweet potato slices over the filling in a circular, slightly overlapping pattern. Dust the potatoes lightly with paprika, then distribute half of the Gruyère and half of the Parmesan over the surface.
Place the remaining potato slices over the cheese in a second overlapping layer. Sprinkle with the rest of the Gruyère and Parmesan, then scatter small pieces of butter across the top. Finish with seasoned salt to taste.
Cover the pie dish with aluminum foil and bake for 30 minutes.
Remove the foil and continue baking for another 25 to 30 minutes, or until the potato slices are completely tender.
For a deeper golden-brown surface, place the uncovered pie beneath the broiler for a few minutes, monitoring it closely to prevent scorching.
Allow the baked shepherd’s pie to rest for approximately 10 minutes before slicing. Garnish with finely chopped Italian parsley immediately before serving.