Martha and her personal chef, Pierre Schaedelin, make delicious paella at her Katonah home.
Place chicken in a large bowl and add 4 tablespoons olive oil. Sprinkle chicken with paprika and 1 teaspoon salt; turn chicken to coat. Cover chicken and let marinate, refrigerated, at least 4 hours and up to overnight.
Bring a large pot of water to a boil; meanwhile, prepare an ice-water bath. With a paring knife, core tomatoes, and score an X on the bottoms. Working in batches, carefully lower tomatoes into boiling water; when skins begin to split, after 30 to 60 seconds, use a slotted spoon to transfer tomatoes to water bath.
When tomatoes are cool, remove skins (use a paring knife, if necessary), and discard. Halve tomatoes. Remove seeds with a spoon, and discard. Finely chop tomatoes.
Cut peppers crosswise into 1/4-inch strips; set aside. Using a mortar and pestle, grind together saffron and 1 tablespoon salt. Add saffron mixture to a medium bowl and add 2 cups chicken stock and cognac. Whisk until well combined; set aside.
If using a charcoal grill, make a fire in your grill. When the charcoals are completely covered in gray ash, hold your hand about 5 inches above the grill grid; count how many seconds you can comfortably leave it there. When you can hold it there for 1 to 2 seconds, you have high heat and are ready to cook. Alternatively, you can cook the paella on a stove over high heat.
Place a 20-inch paella pan with 3-inch sides over desired heat source. Coat the bottom of the pan with olive oil and heat, until pan is very hot, about 5 minutes. Add chicken thighs and cook, turning, until golden brown on all sides, about 8 minutes. Add pork and cook, turning, until browned, about 3 minutes more.
Add peppers, onions, garlic, haricots verts, and tomatoes. Cook, stirring, about 2 minutes. Add calamari, and shrimp, and cook, stirring, about 2 minutes more; add clams and mussels.
Add rice and stir to coat. Add reserved chicken stock mixture and let cook about 1 minute. Add 3 cups of stock and bring to a boil. Let cook, covered with the lid of the grill or aluminum foil, until rice is tender, about 15 minutes, adding more stock as necessary (you may not need to use all the stock).
Add lima beans and peas and cook, until tender, about 3 minutes more. Season with salt and lemon juice; serve immediately.