Pat the chicken dry with paper towels. Season on both sides with 1 teaspoon salt and ¼ teaspoon pepper.
Heat ¼ cup olive oil in a large pot until it shimmers. Add the chicken skin down to the pan over medium-high heat and let cook for about 8 minutes, until golden brown. Flip the chicken and cook for a few minutes on the other side.
Remove the chicken from the pan and add the onions. Cook over medium heat for 5-7 minutes, until translucent.
Meanwhile, chop the mushrooms.
Add the mushrooms to the pan and let cook for 5-10 minutes, until reduced and the liquid has evaporated.
Lower the heat and add the garlic to the pan. Stir in 1 cup broth, garlic powder, and oregano, making sure to scrape the bottom of the pan.
Add the rice and stir to evenly combine everything.
Add the chicken back to the pan, skin side up, and push it in so the meat touches the bottom of the pan.
Pour the rest of the vegetable broth into the pan and stir.
Preheat the oven to 250°F. Cover the pot with its lid and cook the chicken for 1½ to 4 hours. If you want your chicken to be a bit crispier on top, place under the broiler for a few minutes.
Squeeze a lemon wedge over everything just before serving.
