Preheat the oven to 375°F (190°C). Lightly grease a 9x13-inch casserole dish.

Heat the olive oil in a large skillet over medium-high heat. Add the ground beef and cook, breaking it up with a spoon, until browned and no longer pink, about 5 to 7 minutes.

Add the diced onion and cook for 3 to 4 minutes, until softened. Stir in the garlic, salt, black pepper, thyme, and paprika, and cook for 30 seconds more.

Add the butternut squash, uncooked rice, beef broth, and diced tomatoes to the skillet. Stir well to combine, then bring the mixture to a simmer.

Transfer the mixture to the prepared casserole dish and spread it evenly. Cover tightly with foil.

Bake for 45 minutes.

Remove the foil, stir gently, and check that the rice is tender and the squash is fork-tender. If needed, bake uncovered for 5 to 10 minutes more until the liquid is absorbed and everything is fully cooked.

Sprinkle the cheddar cheese and Parmesan evenly over the top. Return to the oven, uncovered, for 5 to 7 minutes, until the cheese is melted and bubbly.

Let the casserole rest for 5 to 10 minutes before serving. Garnish with parsley if desired.