Pat the tuna dry on both sides with paper towels, then brush each filet lightly with sesame oil. Season each tuna steak with Kosher salt. Mix black sesame seeds and white white sesame seeds together on a plate or sheet tray. Firmly press the tuna filets into the sesame seeds.
Whisk together ponzu, mirin, ginger paste, fish sauce, sesame oil, sugar, sriracha, and the juice of lime in a large bowl.
Heat neutral oil in a large nonstick skillet over high heat. When hot, add thinly sliced scallions and chopped garlic cloves, then cook, stirring often. Pour the scallion and garlic mixture into the sauce, then stir well to combine. Gently wipe out the pan.
Return the pan to medium-high heat, then add remaining neutral oil. When just barely smoking, carefully add the tuna fillets. Transfer the seared tuna to a plate. Allow to cool slightly.
Add the cooked soba noodles directly to the sauce, then gently toss to thoroughly mix. Divide the noodles evenly between two bowls.
Thinly cut tuna across the grain into slices, then divide between bowls. Garnish with scallions, Thai red chiles, fresh cilantro, sesame seeds, and lime wedges. Pickled ginger can be added to the bowls or served on the side. Enjoy hot, room temperature, or cold.