In a mixing bowl, combine the cilantro, jalapeno, ginger, garlic, lime juice, soy sauce, sugar, salt, pepper, and 1/4 cup of olive oil. Stir the ingredients together until well incorporated.
Place a large skillet over medium-high heat and coat with the remaining 2 tablespoons of olive oil. Season the tuna pieces generously with salt and pepper. Lay the tuna in the hot oil and sear for 1 minute to form a slight crust; flip and sear the other side 1 minute. Pour half of the cilantro mixture into the pan to coat the fish. Transfer the seared tuna to plates and serve with the sliced avocado and the remaining cilantro sauce drizzled over the whole plate.