Rinse the rice under cool water until mostly clear, then drain well.
Warm the olive oil in a medium saucepan over medium heat.
Sauté the onion until translucent, about 3 to 4 minutes.
Stir in the garlic and oregano; cook until fragrant, about 30 seconds.
Add the drained rice and toast, stirring, for 1 to 2 minutes.
Pour in broth, lemon juice, and zest. Season with salt and pepper; bring to a gentle boil.
Reduce heat to low, cover, and simmer until liquid is absorbed, 14 to 16 minutes.
Remove from heat and rest, covered, for 5 minutes to finish steaming.
Fluff with a fork; fold in butter, dill, and parsley. Taste and adjust seasoning.