In a colander, scrub the mussels well under cool water, discarding any with broken shells. Remove any beards from the mussels by pulling toward the tapered end of the shell until it comes free.

Bring a large pot of generously salted water to a boil, then add the spaghetti and cook until barely al dente (5–7 minutes, about half the recommended cooking time on the package). Reserve 1 cup of the pasta cooking water, then drain.

Meanwhile, make the sauce: To a large, deep skillet set over medium-low heat, add the olive oil and garlic and cook, stirring occasionally, until beginning to brown, 4–6 minutes. Add the tomatoes, season with salt, and turn the heat to medium. Cook, stirring occasionally, until the tomatoes begin to break down and release their juices, 3–4 minutes more. Turn the heat to medium-high and add the mussels and white wine. Cook, shaking the skillet occasionally, until the mussels open, 3–4 minutes, using tongs to transfer the mussels as they open to a medium bowl. (Discard any that remain closed.) Set aside until cool enough to handle, then pull the meat from all but one fourth of the cooked mussels, transfer to a small bowl.

Return the skillet to medium-high heat, then add the pasta and cook, swirling the pan, until the pasta is al dente and coated in sauce, about 4 minutes. (If the pasta seems dry, gradually add enough of the reserved pasta water to make the sauce smooth and silky.) Add the shelled and unshelled mussels and their accumulated juices to the pot and cook until heated through, about 1 minute more. Remove from the heat, sprinkle with parsley, and serve hot.