In a large bowl, combine the tomatoes, garlic, pepper paste, cilantro, cayenne, cumin, lemon juice, and olive oil. Mix thoroughly with a spoon or spatula (do not use a whisk).
Heat a large stockpot over medium-high heat, add the tomato mixture, and cook until the mixture becomes fragrant and tomatoes begin to break down, about 1 minute.
Add the clams, stock, and basturma and bring to boil over high heat. Reduce the heat to simmer, cover, and cook, shaking the pot occasionally, just until all of the clams have opened. Using a slotted spoon, transfer the clams to serving bowls, leaving the broth in the pot.
Add the butter to the broth and check for seasoning. The basturma and the clams carry a good deal of salinity, and the soup will probably not need salt.
Ladle the broth over the clams, garnish each bowl with a handful of cilantro leaves, and serve with thick slices of grilled bread.