Melt butter in a large saucepan over medium heat. Saute onions in butter until tender and lightly browned, about 10 minutes. Add tomatoes, and continue cooking for 10 more minutes, stirring frequently. Add the potato, and 2 cups of water. Season with the bay leaf, garlic and salt. Bring to a boil, then reduce heat and simmer, covered, for about 20 minutes.
Stir in the remaining water, and bring to a boil again. Discard bay leaf, and strain the solids from the broth, reserving both. Puree the vegetables in a food processor or blender, and stir them back into the broth. Bring to a boil, and add the rice. Cover and simmer over low heat for about 15 minutes, or until rice is tender. Serve hot.
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