Warm the olive oil in a large deep skillet or wide saucepan over medium heat.
Add the ground beef to the skillet and cook, breaking it into small pieces with a spatula, for about 5–7 minutes until browned and no longer pink.
Stir in the diced onion and cook for 3–4 minutes, until the onion softens and turns translucent.
Add the minced garlic, dried oregano, dried basil, smoked paprika, salt, and black pepper. Cook for 1 minute, stirring, until the garlic is fragrant and the spices coat the beef.
Pour in the dry orzo pasta, beef broth, and crushed tomatoes. Stir well, making sure the orzo is submerged in the liquid and evenly distributed.
Bring the mixture to a gentle boil, then reduce the heat to low. Cover the skillet with a lid and simmer for 10–12 minutes, stirring once or twice, until the orzo is tender and most of the liquid is absorbed.
Remove the lid and pour in the heavy cream. Stir to combine, then let the sauce gently bubble over low heat for 2–3 minutes to thicken slightly.
Sprinkle in the grated Parmesan cheese and stir until it melts into the tomato cream sauce and becomes smooth.
Taste and adjust seasoning with a little more salt or black pepper if needed.
Turn off the heat and sprinkle the chopped fresh parsley over the top. Give everything a final gentle stir, then let the skillet rest for 2–3 minutes before serving so the sauce can set slightly.