Heat 1 tablespoon oil in 8-inch skillet over medium heat until shimmering. Add panko and cook, stirring frequently, until golden brown, about 4 minutes. Season with salt and pepper to taste. Transfer to plate and let cool.
Bring 4 quarts water to boil in large pot.
Process basil, parsley, capers, anchovies, lemon zest and juice, garlic, mustard, salt, pepper, and remaining ½ cup oil in food processor until smooth, about 1 minute, scraping down sides of bowl as needed. Transfer to large heatproof bowl.
Add pasta and 1 tablespoon salt to boiling water and cook, stirring occasionally, until al dente. Reserve 1 cup pasta cooking water, then drain pasta. While pasta drains, whisk ½ cup reserved pasta cooking water into sauce. Add pasta to sauce and toss gently with tongs, adjusting consistency with remaining reserved pasta cooking water as needed. Sprinkle with panko mixture. Serve, passing Parmesan separately.
