Preheat the oven to 375°F (190°C).
In a large skillet over medium heat, add olive oil. Add the diced onion and minced garlic, cooking until translucent (about 3-4 minutes).
Add the sausage to the skillet, breaking it apart with a spatula. Cook until browned and completely cooked through (about 8-10 minutes). Drain excess fat if necessary.
In a mixing bowl, combine the heavy cream, milk, salt, pepper, and paprika. Stir until well combined.
In the baking dish, layer half of the sliced potatoes evenly on the bottom. Pour half of the cream mixture over the potatoes. Then, add half of the cooked sausage and half of the frozen mixed vegetables (if using).
Repeat the layers with the remaining potatoes, cream mixture, sausage, and mixed vegetables.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.
After 30 minutes, remove the foil and sprinkle the cheddar cheese on top. Return to the oven and bake for an additional 15 minutes, or until the cheese is bubbly and golden brown, and the potatoes are tender.
Allow the casserole to cool for a few minutes before serving.