Bring 4 quarts water to a boil and add 3 tablespoons salt. Set up an ice bath. Blanch basil for 2 minutes in boiling water, then transfer immediately to an ice bath. Cool for 2 minutes, drain, then squeeze excess water from basil. Blend basil and 1 cup olive oil in a blender until well mixed. Strain in a coffee filter or cheesecloth.
Heat cast iron pan over high heat until very hot. Season tuna with salt and pepper. Brush lightly with olive oil. Place steaks in pan and cook until bottom is brown and crusty, about 3 minutes. Flip tuna and cook for 1 minute. (Tuna will be just seared on the outside and raw in the middle.)
Remove to a plate. Drizzle with basil oil and garnish with lemon juice and zest.