In a large heavy-bottomed pot or Dutch oven set over medium heat, melt the butter until foamy. Add the sliced onion and sauté for 4 to 5 minutes, stirring occasionally, until translucent and soft.
Stir in the minced garlic and cook for 30 seconds, just until fragrant. Add the halved cherry tomatoes and cook for 4 to 6 minutes, until they begin to soften and release their juices.
Add the tomato paste, oregano sprigs, and orzo. Stir well to coat the grains evenly with the tomato mixture.
Pour in the water and salt. Bring to a gentle simmer and cook uncovered over medium-low heat for about 8 minutes, stirring occasionally with a wooden spoon or silicone spatula to prevent sticking.
Stir in the heavy cream and continue cooking for another 5 minutes, until the orzo is fully tender and the sauce is creamy and thick.
Remove from the heat and discard the oregano sprigs. Fold in the grated Parmesan and stir until fully melted and incorporated. For a spicy kick, sprinkle with crushed red pepper flakes to taste.
Serve warm, straight from the pot or spooned into shallow bowls. Best enjoyed immediately.