Toast the pine nuts: Heat a dry skillet over medium heat. Add pine nuts and toast for 3-4 minutes, shaking the pan occasionally, until golden brown and fragrant. Watch closely to prevent burning. Remove from heat.
Mellow the garlic: In the same skillet, add a small drizzle of olive oil and cook garlic cloves over low heat for 2 minutes until softened but not browned. This removes the sharp raw edge.
Make the Genovese sauce: In a food processor or blender, combine basil leaves, toasted pine nuts, cooked garlic, Parmesan cheese, lemon juice, and half the olive oil. Pulse until combined but still textured. With the motor running, slowly drizzle in remaining olive oil until sauce is smooth and pourable. Season with salt and pepper to taste.
Prepare the tuna mixture: In a medium bowl, gently break apart the tuna, keeping some nice chunks intact. Don't drain the oil—it adds flavor and moisture! Fold in capers and sliced red onion.
Combine and rest: Add about half of the Genovese sauce to the tuna mixture and gently fold together. Let the mixture rest for at least 15 minutes to allow flavors to meld. (Trust me on this—it makes a huge difference!)
Serve: Spoon tuna mixture onto crusty Italian bread, over fresh arugula, or enjoy it however you like! Drizzle with remaining Genovese sauce and garnish with fresh basil and cherry tomatoes if desired.