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Step 1
For the Sofrito: Place dried peppers (if using) in a medium heatproof bowl and cover with boiling water (if not using, skip to Step 3). Place a weight or wet paper towel on top to help submerge the peppers. Let stand until peppers are fully softened, 30 minutes to 1 hour. If the peppers are very stubborn (as thick-skinned ñoras can be), you may need to tear a small hole in them to let water penetrate inside.
Step 2
Drain peppers and discard stems and seeds. Using a paring knife, carefully scrape the flesh from the skins. Discard skins.
Step 3
In a 3-quart saucepan, heat oil over medium-high heat until shimmering. Add garlic, onion, red pepper, and scraped rehydrated chili flesh (if using), season lightly with salt, and cook, stirring, until vegetables have released their liquid and are beginning to brown lightly on the bottom of the pan, about 6 minutes.
Step 4
Lower heat to medium-low and continue cooking, stirring and scraping frequently, until sofrito is sweet to the taste and a deep golden brown color, about 30 minutes longer. Stir in tomato paste and cook for 2 minutes longer. You should have about 1 cup. You can refrigerate the sofrito in an airtight container for up to 5 days. (Any extra sofrito not used in this recipe can be used as a flavor base for soups, sauces, braises, stews, and more.)
Step 5
For the Paella: In a 10-inch paella pan or straight-sided stainless steel sauté pan, heat oil over medium-high heat until shimmering.
Step 6
Season chicken all over with salt, then add to pan and cook, turning, until deeply browned on both sides, about 8 minutes.
Step 7
Add sofrito, paprika, and saffron, and cook, stirring and scraping until well mixed and sizzling.
Step 8
Add stock (or water) and bring to a rolling boil. Season lightly with salt. Sprinkle in rice all over, making sure all grains are submerged and none are stuck on top of the pieces of chicken. Using your spatula, gently swirl the liquid around to distribute the rice evenly. Return to a boil, then reduce heat to medium-low.
Step 9
Cook for 8 minutes without stirring, then season shrimp with salt and nestle around the chicken thighs. Continue cooking until the rice is just al dente and the liquid has fully been absorbed, about 8 minutes longer; turn the shrimp during this time to cook them until pink on both sides. Reduce heat to low at any point to prevent scorching on bottom (though browned and crispy rice on the bottom is desirable).
Step 10
If the liquid cooks off and the rice isn't done enough, add more boiling-hot stock or water in small additions and continue cooking until the rice reaches the desired doneness. You can also use a spoon to carefully dig into the paella and check the bottom of the pan to make sure nothing is burning.
Step 11
When the rice is perfectly cooked and the liquid is fully absorbed, remove from heat and let rest 5 minutes before serving with lemon wedges.