Slice Tofu into 6-8 pieces. Place them on paper towels over a plate and microwave for 2 minutes. Change to new paper towels and microwave for 2 more minutes. Change to new paper towels again and let Tofu cool.
Cook spinach in boiling water for a minute. Wash under cold water and squeeze water out very well. Cut into 1" long bunches.
In a medium pot, heat Dashi to boil, add carrot and Konnyaku, and cook for 2-3 minutes. Add Mirin and soy sauce and cook until liquid is almost gone. Let it cool, then add spinach and mix.
Grind sesame seeds, and mix with soy sauce and sugar.
Mash Tofu and mix in sesame sauce. Then add cooked vegetables.