Heat the butter in a medium heavy saucepan over low heat. Add the onion and pepper and a large pinch of salt and stir to coat. Cook gently, stirring frequently, until softened, about 5 minutes. (Do not let the vegetables brown -- if necessary, add a splash of water to prevent this.)
Add the tomatoes and another large pinch of salt to the pan and stir to combine. Raise the heat so the mixture bubbles steadily and cook for 5 to 7 minutes, until you have what resembles a thick sauce.
Stir in the rice, 2 1/2 cups cold water and a couple more pinches of salt. Bring to a brisk simmer and cook uncovered for 5 to 8 minutes without stirring, until the liquid on the surface is mostly gone. Stir the rice briefly, cover and turn the heat down as low as it will go. Cook the rice, without removing the lid, for 25 minutes. Turn off the heat and let the pot sit covered for 5 minutes. Fluff the rice with a fork and serve.