Heat the oven to 375°F. If not using an oven-safe skillet, lightly oil a 9×13-inch baking dish and set aside.
Warm the olive oil in a 12-inch oven-safe skillet or Dutch oven over medium heat. Add the onion and cook, stirring, until translucent and tender, 5–7 minutes. Stir in the garlic and cook until fragrant, 30–45 seconds.
Add the orzo and cook, stirring, to lightly toast the pasta, 1–2 minutes. Stir in the tomato paste and cook 1 minute to caramelize.
Add the canned diced tomatoes with their juices, vegetable broth, dried oregano, bay leaf, red pepper flakes, kosher salt, and black pepper. Bring to a gentle simmer, 2–3 minutes, stirring to combine.
If using a baking dish, transfer the mixture to the prepared dish. Spread the orzo into an even layer and cover tightly with a lid or foil.
Bake until the orzo is just tender and most of the liquid is absorbed, 20–25 minutes, stirring once halfway; the edges should be bubbling and the pasta should have a slight bite.
Remove from the oven, discard the bay leaf, and let rest 5 minutes. Stir to loosen, taste, and adjust seasoning.
Serve hot, topped with feta cheese and parsley, with lemon wedges for squeezing.