Make miso marinade.
In a small saucepan, mix together 1 tbsp. light miso, 2 tbsp. mirin, and 1 tbsp. sugar over low to medium heat and allow sugar to dissolve. When the mixture is well combined, let mixture cool for at least 15 minutes.
Sous vide salmon and eggs.
When the miso mixture has cooled, pour into ziplock bag or a vacuum sealer bag along with the salmon filet (preferably with no skin). Set up your water bath and place sealed bag into the bath. Set the precision cooker timer at 120°F (48°C) for 45 minutes. Drop your eggs into the same water bath. When the salmon is done, remove from water bath and leave egg in there. Set to 145°F (62°C) for another 10 minutes. Remove from water bath.
Gently crack the egg and begin to peel away shell. Peel about half of the shell off and very gently pour the egg out onto a small ramekin or bowl. If the egg white is not set enough to your liking, drop egg into a small pot filled with water at a low simmer to finish poaching.
Mix together ingredients for mentsuyu.
In a small saucepan, prepare the mentsuyu sauce. Mix together ⅓ cup soy sauce, 2 tsp. sugar, packet of dashi, 3 tbsp. sake and 4 tbsp. of mirin. Allow sugar to dissolve over low to low medium heat. When mixture is combined well, remove from heat and allow cool for about 15 minutes.
After mentsuyu has cooled, add scallion and sliced shiitake mushrooms to the sauce.
Boil cha soba noodles in a pot of water according to instructions of the packet. When noodles are al dente in texture, remove from water and drain with strainer. To cool noodles down and stop cooking, prepare an ice bath in a bowl with water and ice and put noodles into the bowl. Swirl around until noodles are cooled. Strain again and portion the noodles onto serving plates or bowls.
Assemble and serve.
Flake the salmon into little bits and place on top of the soba noodles. Place egg in a small bowl next to mentsuyu sauce. Top the noodles with sesame seeds or nori flakes. To eat, simply drop the egg into the mentsuyu and mix. Take a strand of noodle, dip it into the sauce, and slurp! Congrats, you just made zaru soba.