Rinse the mussels under cold water, scrubbing shells and pulling away any beards. Discard any with cracked shells or that remain open when tapped; keep chilled.
Heat the olive oil in a wide, heavy pot over medium heat. Add the onion and cook, stirring, until translucent and sweet, 5–7 minutes.
Stir in the garlic and red pepper flakes and cook until fragrant, 30–60 seconds.
Pour in the white wine and simmer until the alcohol aroma cooks off and the liquid is reduced by about half, 2–3 minutes.
Add the crushed tomatoes, kosher salt, and black pepper. Bring to a lively simmer and cook, stirring occasionally, until slightly thickened and well flavored, 10–15 minutes.
Add the mussels, toss to coat in the sauce, spread them in an even layer, then cover. Cook, shaking the pot once or twice, until most shells have opened and the mussels are plump, 5–7 minutes.
Uncover, discard any mussels that did not open, and stir in the chopped parsley. Taste the sauce and adjust seasoning as needed.
Ladle mussels and red sauce into warm bowls, sprinkle with parsley (for serving), and serve immediately with crusty bread (for serving).