Heat olive oil in a large skillet over medium heat. Toast orzo for 2-3 minutes until golden. Add onion and garlic, sauté until softened. Stir in oregano, vegetable broth, salt, and pepper. Bring to a simmer and cook for 8-10 minutes until orzo is tender (reserve a bit of liquid if needed). Add spinach in batches, stirring until wilted. Remove from heat, fold in feta and lemon zest. Adjust seasoning and toss with lemon juice.