Prepare the tuna. Pat the tuna dry on both sides with paper towels, then brush each filet lightly with sesame oil. Season each tuna steak with ½ tsp Kosher salt. Mix ¼ cup black sesame seeds and ¼ cup white white sesame seeds together on a plate or sheet tray. Firmly press the tuna filets into the sesame seeds to coat on all sides.
Make the sauce. Whisk together ⅓ cup of ponzu, 2 Tbsp mirin, 2 tsp ginger paste, 2 tsp fish sauce, 2 tsp sesame oil, 2 tsp sugar, 2 tsp sriracha, and the juice of 1 lime in a large bowl.
Sauté the aromatics. Heat 2 Tbsp neutral oil in a large nonstick skillet over high heat. When hot, add thinly sliced scallions and 3 chopped garlic cloves, then cook, stirring often, for 1-2 minutes, or until very fragrant. Pour the scallion and garlic mixture into the sauce, then stir well to combine. Gently wipe out the pan.
Sear the tuna. Return the pan to medium-high heat, then add remaining 2 Tbsp neutral oil. When just barely smoking, carefully add the tuna fillets, cooking for 30-60 seconds per side for rare, or 1-2 minutes per side for medium. Transfer the seared tuna to a plate. Allow to cool slightly.
Dress the noodles. Add the cooked soba noodles directly to the sauce, then gently toss to thoroughly mix. Divide the noodles evenly between two bowls.
Assemble, then serve. Thinly cut tuna across the grain into slices about ¼ -inch thick, 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.