Heat oven to 375 degrees. On parchment-lined foil, drizzle garlic with oil; tightly seal. Bake until tender, about 1 hour. Once cool, remove cloves from papery skin and set aside.
In a large pot, heat 1 tablespoon butter over medium heat; add thyme and roasted garlic cloves. Cook 1 to 2 minutes, then add wine and season with salt. Bring to a boil, add mussels, and reduce heat to medium. Cook, covered and undisturbed, until shells have opened, 6 to 8 minutes.
Stir mussels and, with a slotted spoon, transfer to a warm serving bowl. (Discard unopened shells.) Return broth to a boil and reduce by half. Whisk in remaining 3 tablespoons butter and parsley. Ladle sauce over mussels and serve immediately.
Mussels take on a lusty new accent when steamed in fruity red wine infused with roasted garlic and thyme. A green salad and hunks of crusty bread complete this postcard from summer.