Rinse and scrub the clams under a thin stream of cold water. Discard any that are open or broken. Drain well.
Place the chiles, tomatoes and garlic cloves in a medium saucepan, cover with water and bring to a boil over medium high heat. Cook for 10 to 12 minutes, until the chiles have plumped and rehydrated and the garlic and tomatoes are fully cooked, soft and mushy, but not falling apart. Using a slotted spoon, transfer the tomatoes, chiles and garlic to a blender, along with 1 cup of the cooking liquid, and allow to cool slightly. Add the cumin, oregano and 1 teaspoon salt. Puree until completely smooth. Set aside.
Heat 2 tablespoons olive oil and 2 tablespoons butter over medium-high heat in a large wide casserole or lidded sauté pan. When the butter begins to foam add the onion, bell pepper, leek and carrot, and cook, stirring often, for about 5 to 6 minutes, until the vegetables have fully softened and begun to lightly brown along the edges. Stir in the wine or beer and 1/2 teaspoon salt, and simmer until the wine or beer has just about evaporated, about 4 to 5 minutes. The vegetables should be quite soft and moist but not wet.
Pour the tomato puree over the vegetables, bring to a boil and add all the clams. Cover the pot, reduce the heat to medium and cook for 7 to 8 minutes, until the shells open. Turn off heat and leave undisturbed for 5 more minutes. Uncover and, using a slotted spoon or tongs, remove all the clams and place in a bowl. Transfer the sauce and vegetables to a bowl or a large heatproof measuring cup and wipe the casserole or sauté pan clean. Add enough water or broth to the sauce to measure 5 cups.
Remove about 3 dozen clams from the shells and discard the shells.
Heat the remaining 3 tablespoons olive oil over medium-high heat in the casserole or sauté pan until hot but not smoking. Add the rice and cook, stirring often, until it crackles, becomes milky white, and feels heavier as you stir it, about 3 to 4 minutes. Don’t let it brown. Stir in the reserved sauce and veggies and the remaining teaspoon salt. Stir well, add all the clams, both shelled and those still in their shells, bring back to a boil, cover and reduce heat to low. Cook for 15 minutes, until most of the liquid has evaporated and the rice has cooked. Taste the rice, and if it seems a bit too dente or not fully cooked and all of the liquid has almost evaporated, add another 1/4 to 1/2 cup water or broth, scrape the bottom, cover and cook for a few more minutes.
When ready to serve fluff with a fork, garnish with fresh parsley or cilantro or both and dig in.