Season the chicken with the salt, pepper, cumin, oregano, Italian seasoning, and smoked paprika.
Heat the oil in a large Dutch oven or deep skillet over medium-high. Cook the chicken until browned, 5 to 7 minutes. Transfer to a plate.
Reduce the heat to medium. Melt the butter, then add the onion and tomatoes. Cook until the onion is soft and the tomatoes have broken down, 8 to 10 minutes.
Stir in half the garlic and cook for 30 seconds. Add the tomato paste and cook until slightly darkened, about 1 minute.
Add the wine and scrape up any browned bits. Simmer until nearly evaporated.
Stir in the orzo and cook for 1 to 2 minutes. Add the stock and return the chicken and any juices to the pan. Simmer, stirring often, until the orzo is tender and most of the liquid has been absorbed, 10 to 12 minutes.
Stir in the cream and remaining garlic. Cook until the sauce thickens slightly, 2 to 3 minutes.
Remove from the heat and stir in the Parmesan until melted. Season to taste with salt and pepper. Add the red pepper flakes or lemon juice, if using, and serve with more Parmesan.