Heat 2 tablespoons olive oil in a large skillet over medium heat. Add the diced onion and cook until softened and just starting to turn golden at the edges, about 5 minutes. Stir in the garlic and oregano and cook until fragrant, 30 seconds to 1 minute. Do not let the garlic brown.

Add the rinsed rice to the skillet and stir to coat in the oil, cooking for 1 minute until the grains look slightly translucent at the tips. Pour in the broth and add the drained beans. Stir once, bring to a boil, then reduce heat to low, cover tightly, and simmer for 18 minutes until the rice is tender and liquid is absorbed.

Remove from heat and let stand covered for 5 minutes. Uncover and fluff with a fork. Stir in the lemon zest, lemon juice, remaining 1 tablespoon olive oil, and chopped parsley. Taste and adjust salt if needed - the broth and feta will add salt, so start conservatively.

Transfer to shallow bowls and top with crumbled feta if using. Serve warm or at room temperature with extra lemon wedges on the side.