1. Coat the bottom of a large skillet (10-inch) with 2 tablespoons of oil and place it over medium to medium-high heat. When the oil is hot, add the mushrooms and cook approximately 12 minutes, flipping a few times, until lightly browned on both sides, adjusting the heat as necessary to prevent burning. Remove the mushrooms from the skillet and transfer to a plate.

2. Add the remaining tablespoon of oil to the skillet and adjust heat to medium. When hot, add the onion and sauté, stirring occasionally, until soft and translucent, about 5 minutes. Add the garlic, stir, and cook about 2 minutes more, until fragrant.

3. Stir in the tomatoes, vinegar, and paprika (and saffron if using). Increase the heat and bring the liquid to a boil. As soon as it comes to a boil, reduce the heat to low and allow the mixture to simmer until almost all the liquid cooks off, about 8 minutes, stirring occasionally.

4. Return the mushrooms to the skillet and add the broth, rice, and salt. Stir to combine, increase the heat to bring the liquid to a simmer then reduce the heat to maintain the simmer and start timing. Allow to cook, uncovered and without stirring, for 10 minutes. After 10 minutes, add the peas, give the mixture a quick stir to redistribute the rice, smooth out the top, then allow to simmer for another 10 minutes, without stirring. Use a spatula and turn the rice, scraping the rice from the bottom of the skillet lifting and turning it; smooth out the top and let simmer for another 5 minutes without stirring. Note: Over-stirring the rice will cause the rice to become creamy like risotto rather than paella. Adjust the temperature if needed. The rice should brown a little on the bottom, but not burn.

5. Once done, use the spatula again and turn the rice, scraping from the bottom and lifting to turn it. Remove the skillet from the heat and allow it to sit for 5 minutes. Sprinkle with parsley and sliced green onions and serve with lemon wedges on the side.