In a medium saucepan, combine vegetable broth and saffron threads, and bring to a simmer; keep warm over low heat.
Heat 2 tablespoons olive oil in a paella pan or large skillet over medium heat.
Sauté onion, bell pepper, and mushrooms (if using) until softened, about 3-5 minutes.
Add garlic, sauté for another minute, then stir in tomatoes, smoked paprika, sweet paprika, and thyme, cooking for 1-2 minutes.
Add rice and remaining tablespoon olive oil, stirring to coat and toast rice for 1 minute.
Slowly add the broth mixture, season with salt and pepper, and avoid stirring from this point.
Bring to a heavy simmer over medium-high heat for 1-2 minutes, then reduce heat to medium-low and simmer for 15-20 minutes until rice is al dente, rotating pan occasionally.
As the broth is absorbed, listen for a crackling sound and check for socarrat formation—the desired golden, crispy crust on the bottom.
Once the broth is nearly absorbed, scatter peas, chickpeas, and garnish options like parsley oil over the top without stirring, cover with foil, and let rest for 5-8 minutes.
Serve with lemon wedges and optional garnishes.