Begin by preheating your oven to 375°F (190°C). This temperature is the sweet spot that allows the sweet potatoes to cook through without burning, a lesson I learned after a few too many overly caramelized edges.

Bring a large pot of salted water to a boil. Carefully add the sweet potato rounds and cook for about 5 minutes until just tender. They should offer slight resistance when pierced with a fork. Initially, I overcooked them, which resulted in a mushy layer that didn't hold up in the casserole. Drain and set aside.

In a large skillet, heat the olive oil over medium heat. Add the diced onion and cook until translucent, about 3 minutes. Stir in the minced garlic and cook for another minute until fragrant. It's important not to let the garlic brown, as it can introduce a bitter note to the dish.

Add the ground beef to the skillet, breaking it apart with a wooden spoon. Cook until browned and no longer pink, seasoning with salt, pepper, thyme, and smoked paprika. The spices should be aromatic and well incorporated into the meat. I've found that adding them at this stage helps to infuse the beef with their full flavor.

Stir in the tomato paste and cook for 2 minutes. Then, pour in the beef stock and Worcestershire sauce, scraping any browned bits from the bottom of the skillet. Allow the mixture to simmer for about 5 minutes until slightly thickened. This creates a rich, savory base that complements the sweetness of the potatoes. In my early attempts, I skimped on the simmering, which resulted in a less cohesive flavor profile.

Fold in the frozen peas and carrots, and remove from heat. The residual warmth will thaw them without overcooking, preserving their texture and color. I once added them too early, and they turned mushy during the baking process.

In a greased 9x13-inch baking dish, layer half of the sweet potato rounds in an even layer. Spoon the ground beef mixture over the sweet potatoes, then top with the remaining sweet potato rounds. I've learned that this layering technique is crucial for even distribution of flavors and textures.

Sprinkle the shredded cheddar cheese evenly over the top layer of sweet potatoes. The cheese will melt into a golden, bubbly crust that's visually appealing and adds a sharp contrast to the dish's sweetness.

Bake in the preheated oven for 25-30 minutes, or until the cheese is melted and the edges are crisping up. The casserole should be heated through, and the sweet potatoes fork-tender. I've found that covering the dish with foil for the first 15 minutes prevents the cheese from over-browning, a tip that's saved many a casserole top.

Let the casserole rest for 5 minutes before serving. This resting period allows the layers to set, making it easier to slice and ensuring that each serving holds together beautifully on the plate.