Blanch basil and spinach leaves in boiling water for 30 seconds, then immediately plunge into ice water. Squeeze out excess water and chop roughly. In a food processor, combine mayonnaise, wasabi, garlic, olive oil, blanched herbs, and salt. Blend until completely smooth and vibrant green. Refrigerate while preparing other components.

Remove tuna from refrigeration 15 minutes before cooking to bring closer to room temperature. Pat completely dry with paper towels. Season generously with salt and pepper, then press sesame seeds into both sides.

Heat cast-iron skillet over medium-high heat until you see wisps of smoke. Add sesame oil and immediately place tuna in pan. Sear exactly 1 minute per side without moving the fish. The cooked portion should extend about 1/8 inch into the tuna while center remains pink.

Transfer tuna to cutting board and let rest 3 minutes before slicing into 1/4-inch strips. The tuna should be golden outside with a ruby-red center. Slice against the grain with a sharp knife.

Place bamboo mat on work surface. Keep a bowl of warm water nearby for wetting hands. Have all ingredients organized and easily accessible for assembly.

Place half sheet of nori on bamboo mat, glossy side down. With wet hands, spread a thin layer of sushi rice over lower two-thirds of nori, leaving 1-inch border at top. Arrange tuna, avocado, and cucumber in a line across the center of rice.

Using bamboo mat, lift the edge closest to you and roll over the filling, tucking tightly. Continue rolling while pulling mat away from you. Apply gentle, even pressure to create a tight roll. Seal the edge with a dab of water.

Using a sharp, clean knife, cut each roll into 6-8 pieces, wiping knife between cuts. Arrange on serving plate and garnish with additional sesame seeds. Serve immediately with basil aioli, soy sauce, and pickled ginger.