Holding mussels under cool running water, scrub with a stiff sponge or vegetable brush, then debeard: grip the tough fibers extending from the shell and pull to remove. Discard beards.
Steep saffron in wine for 10 minutes. (Saffron is soluble in water, not fat, so it won’t release its color or flavor if added directly to the butter.) Meanwhile, melt butter over medium-high heat in a shallow stockpot. Once it’s foamy, add shallots, garlic, and 1/2 teaspoon salt. Cook until shallots are transparent and garlic is soft, about 3 minutes, stirring every so often to keep garlic from scorching. Pour in wine and saffron, then add tomatoes and return to a simmer, stirring once or twice.
Add mussels and cover tightly. Cook until all mussels open, about 6 minutes, stirring once about halfway through. Discard any unopened mussels. If using wild mussels, strain broth through a cheesecloth-lined sieve to remove any sand, if necessary. Taste the broth and season with salt and pepper.
Sprinkle with parsley before ladling mussels and broth into bowls.