Place the canned whole peeled tomatoes in a small food processor or blender.
Pulse until the tomatoes are smooth. If using fresh tomatoes, remove the stems first, then blend until smooth.
Pat the beef cubes dry with paper towels.
Season the beef with salt, black pepper, ground allspice, and a pinch of nutmeg.
Rub the seasonings evenly over all sides of the meat.
Heat the olive oil in a sauté pan over medium-high heat.
Add the seasoned beef to the pan.
Brown the beef on all sides, working in batches if necessary to avoid overcrowding the pan.
Reduce the heat to medium.
Add the minced red onion to the pan.
Cook for about 1 minute, stirring with a wooden spoon and scraping the bottom of the pan.
Add the tomato paste.
Cook for 1 to 2 minutes, stirring constantly, until the tomato paste darkens slightly and begins to caramelize.
Pour in the red wine.
Stir well, scraping the bottom of the pan to deglaze.
Cook for about 1 minute, allowing the alcohol to evaporate.
Stir in the blended tomatoes.
Add the beef or vegetable stock.
Pour in 2 cups of boiling water.
Add the sweet paprika and dried bay leaves.
Stir to combine.
Bring the mixture to a simmer.
Cover the pan with a lid.
Reduce the heat to low.
Simmer for about 1 hour, or until the beef is tender.
Add the remaining 2 cups of boiling water to the pan.
Season with additional salt and black pepper to taste.
Add the orzo pasta.
Cover the pan again.
Continue simmering for about 20 minutes, stirring occasionally to prevent the orzo from sticking to the bottom of the pan.
If the orzo remains too firm, add about 1/4 cup additional water as needed.
Remove the pan from the heat.
Allow the dish to rest for 1 to 2 minutes, as the orzo will continue absorbing liquid and the sauce will thicken.
Remove and discard the bay leaves before serving.
Serve immediately with grated Kefalotyri cheese, if desired.