For the rice:
Heat a drizzle of extra-virgin olive oil and 2 tablespoons butter over medium heat in a saucepot with tight fitting lid. To the melted butter, add the orzo and lightly toast. Add the onion and cook to soften, 5 minutes. Stir in the rice and 1 1/2 cups of stock and bring to a boil. Reduce heat, cover, and simmer for 15 minutes.
Preheat the broiler.
For the beef:
Heat a cast iron griddle or a grill pan over medium-high heat. Coat flank steaks in extra-virgin olive oil and season liberally with salt and pepper. When the grill is very hot, cook the meat 10 to 12 minutes for medium-rare or 15 minutes for medium, turning occasionally.
When the meat has been cooking for about 5 minutes, start the sauce in a small saucepot over medium heat. Add 2 tablespoons extra-virgin olive oil, garlic, shallot, chile pepper, and oregano. Stir 2 to 3 minutes, and then add the butter. When the butter melts, stir in the lemon juice and remove from heat.
For the rice:
Add the remaining splash of stock along with the spinach to a food processor and process to a fine chop. Stir the spinach into the rice and season with nutmeg, salt, and pepper. Cover, turn off the heat, and let stand 2 more minutes. Fluff the rice with fork and stir in the feta.
For the tomatoes:
Season halved tomatoes with salt and pepper and top with parsley. Drizzle the tomatoes liberally with extra-virgin olive oil and broil 3 to 4 minutes.
Allow the meat to rest a bit then very thinly slice against the grain. Serve the sliced steak with a side of rice, a spoon of sauce over top, and a 2 tomato halves per person.
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