Add 2 tablespoons of olive oil in a large skillet with and place it over medium heat. When it's hot, add the mushrooms and cook them for 7 minutes, stirring occasionally, until lightly golden. Remove the mushrooms from the skillet and transfer them to a plate. Set aside.
Add the remaining tablespoon of oil into the skillet and when it's hot, add the onion. Sauté until soft and translucent, for about 4 minutes, then add the garlic and cook for about 2 minutes more, until fragrant. Add sliced Capia pepper and cook for 3 more minutes.
Add the wine, paprika, chili, and saffron. Bring the liquid to a boil. Lower the heat and allow let it simmer for about 10 minutes, stirring occasionally.
Return the mushrooms to the skillet and stir in the broth/water, rice, peas, olives. Cook uncovered for 10 minutes.
Stir and add the Nori, dry tomatoes, salt, and pepper to taste. Let it simmer for about 10 minutes, until the rice is soft.
Remove the skillet from the heat and allow it to sit for 5 minutes. Sprinkle with parsley and serve with lemon wedges.