Bring a large pot of water to a boil. Salt the water, add the pasta, and cook to al dente.
Place the basil, 3 tablespoons toasted sesame seeds, tamari, garlic, lime juice, and chile into a food processor. Pulse into a paste. Drizzle in the extra-virgin olive oil. Pour the pesto into a large bowl and add a splash of starchy cooking water. Drain the pasta, add to the sauce, and toss to combine. Drizzle with sesame oil, garnish with scallions and the remaining 2 tablespoons toasted sesame seeds.