Make the pickled cucumber. Thinly slice the cucumber into 1/16-inch thick slices. Whisk together the boiling water with rice vinegar, sugar, and salt, stirring until the sugar has dissolved. Pour over the cucumber slices and let sit for 30 minutes.
Meanwhile, make the tuna marinade. Combine ¼ cup olive oil with cilantro, basil, zest and juice of 1 lime, jalapeno, ginger, garlic, soy sauce, red wine vinegar, and 2 teaspoon sugar, whisking until combined. Reserve ¼ of the sauce for serving and pour the remaining over the tuna. Let sit for 15 minutes.
Preheat a grill to high heat. Cut the avocado in half and remove the pit. Brush the cut side with olive oil and place it on the grill. Cook until grill marks appear. Set aside.
Heat a medium saute pan over high heat. Sear the tuna until browned on both sides but still pink in the middle. Remove from heat and let sit for 10 minutes. Slice the tuna and transfer to a plate.
Serve the seared tuna with the reserved sauce, pickled cucumber, grilled avocado, and rice if desired.