Prepare the following, adding each to the same medium bowl as you complete it: Finely grate 6 garlic cloves; pick the leaves from 6 fresh rosemary sprigs, then finely chop (4 to 6 tablespoons); add 3 tablespoons olive oil and 2 tablespoons Dijon mustard, 1 tablespoon kosher salt, and 1 teaspoon black pepper, and stir to combine.
Place 2 lamb racks on a rimmed baking sheet (lined with aluminum foil for easier cleanup if desired). Spread the rosemary rub all over the lamb racks (about ¼ cup each). Position the racks so the rib bones point down. Let sit at room temperature for 1 hour. (Alternatively, cover and refrigerate for up to 12 hours; let sit at room temperature for 1 hour before roasting uncovered.) After 30 minutes, arrange a rack in the upper third of the oven and heat the oven to 450ºF.
Roast the lamb for 15 minutes. Flip the racks and roast until the thickest part registers 130ºF on an instant-read thermometer for medium-rare, about 10 minutes longer.
Transfer the racks to a clean cutting board. Let rest for at least 10 minutes. To carve, cut between the rib bones into individual chops. Lightly sprinkle with flaky salt if desired. Place on a serving platter and garnish with more fresh rosemary if desired.
