Preheat the oven to 375°F (190°C). Preheating ensures the casserole begins cooking immediately and the rice will absorb heat evenly during the bake.

Warm a 12-inch (30 cm) ovenproof skillet or braiser over medium-high heat and add the olive oil. Add the ground beef and season with 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper. Brown the beef, breaking it up with a spatula, until nicely caramelized (6–8 minutes). Browning develops Maillard flavors that give the dish its deep, savory backbone; do not crowd the pan or the meat will steam instead of brown.

Use a slotted spoon to transfer browned beef to a bowl, leaving 1–2 tablespoons fat in the pan. Add the butter and the diced onion; cook over medium heat until the onion is soft and translucent (4–5 minutes). The butter helps carry flavor and softens the onion without burning.

Add the minced garlic and cook for 30–45 seconds until fragrant — this short step prevents garlic from turning bitter. Stir in the tomato paste and smoked paprika and cook 60–90 seconds, stirring constantly — to 'toast' the paste and paprika. Toasting these ingredients blooms their sugars and spices, deepening flavor and preventing a raw tomato taste.

Return the browned beef to the pan. Stir in the Worcestershire sauce and the remaining 1 teaspoon kosher salt and 1/2 teaspoon black pepper. Deglaze with the beef broth, scraping up browned fond from the bottom with a wooden spoon. The fond contains concentrated flavor; loosening it into the liquid builds a richer sauce base.

Add the uncooked rice to the beef mixture and stir to coat each grain with the sauce. Pour in the milk and bring the mixture to a gentle simmer. Using a mix of milk and broth creates a creamier, risotto-like texture when baked without the need for constant stirring.

Stir in the shredded cheddar and grated Parmesan, leaving about 1/2 cup cheddar aside for the topping. Mixing some cheese in now helps thicken the liquid and gives an even, creamy distribution of cheese throughout the rice.

Cover the skillet or transfer everything to a buttered 9x13-inch (23x33 cm) baking dish and cover tightly with a lid or foil. Bake for 35–40 minutes, until the rice is tender and most of the liquid has been absorbed. Covering traps steam so the rice cooks evenly; check at 30 minutes if your oven runs hot.

Remove the cover, sprinkle the reserved 1/2 cup cheddar evenly over the top, and return to the oven uncovered for 8–10 minutes, or until the cheese is melted and bubbling and edges are golden. If you want a blistered top, switch to broil for 1–2 minutes — watch closely to avoid burning.

Rest the casserole for 8–10 minutes before serving so the rice sets slightly and flavors meld. Garnish with chopped parsley and a few grinds of black pepper. Resting also makes portioning cleaner and prevents the dish from being overly runny on the plate.