Preheat oven to 350°F or preheat grill to medium.
Coat a large saute pan, wok, paella pan, or cast iron skillet generously with oil, and heat over a medium flame. Add shallots, leek, red peppers, and fennel, and cook for 20 minutes until very soft and beginning to brown.
Add anchos and tomatoes. Continue cooking, stirring occasionally, until most of water has cooked out of the sofrito and the mixture is thick and fragrant. Add garlic and continue cooking for 1 to 2 minutes until softened.
Push the sofrito to the side of the pan and add a bit more oil. Sauté mushrooms until browned. Combine sofrito and mushrooms.
Add smoked paprika, saffron, crushed red pepper, and wine.
Add rice, broth and stir to combine. (This is the last time you will stir the dish, so make it count!)
Cover with foil or a lid and decrease the heat to medium low. Once the rice is swollen and tender, 20 to 30 minutes, scatter chickpeas, parsley, olives, tomatoes, and lemon slices across the top. If the rice is still firm, you may need to add a bit more liquid, so feel free to drizzle more broth in and continue cooking.
Keep warm until ready to serve.