Bloom the saffron. Place the saffron threads in a small bowl and cover with ¼ cup of warm water. Let them soak for at least 10 minutes. Start cooking while they bloom — the saffron takes care of itself.
Brown the mushrooms. Coat the bottom of your paella pan with 3 tablespoons of olive oil over medium heat. When hot, add the mushrooms and season with salt. Cook for about 10 minutes, flipping once halfway through, until lightly browned on both sides. Transfer to a plate and set aside.
Soften the aromatics. Add the remaining tablespoon of olive oil to the pan. Add the diced onion and bell pepper and sauté for about 5 minutes, stirring frequently, until they start to soften.
Add the garlic. Push the onion and pepper to the side of the pan. Add the minced garlic into the cleared space and sauté for 1 minute, stirring constantly, until fragrant.
Build the flavor base. Stir in the diced tomatoes, white wine, sweet paprika, smoked paprika, and the saffron along with its soaking water. Raise the heat and bring to a boil, then reduce and simmer for about 5 minutes until the liquid reduces by roughly half.
Add rice and broth. Return the mushrooms to the pan. Stir in the rice, vegetable broth, and olives. Season with salt and pepper. Raise the heat to bring everything to a boil, stirring occasionally as it heats. Once boiling, reduce to a low simmer and stop stirring completely from this point forward.
Cook the rice uncovered. Simmer uncovered for about 20 minutes, repositioning and wiggling the pan occasionally for even heat distribution. The rice should become tender and the bottom should develop a slight char. If it dries out before the rice is cooked, add water ½ cup at a time.
Add the peas. Sprinkle thawed peas evenly over the top of the paella and let them cook for 1–2 minutes until warmed through.
Rest the paella. Remove from heat. Cover tightly with a lid or foil and let it rest for 5 minutes. This step is not optional it lets the steam redistribute and finishes the rice perfectly.
Serve. Uncover, season with salt and pepper to taste, scatter fresh parsley generously over the top, and serve directly from the pan with lemon wedges on the side.
