Wrap the tofu in kitchen paper towels, put on a weight that won't crush them (such as a flat plate) and drain out the excess water (about 15 minutes).
Finely julienne the carrot, shred the shimeji mushrooms into small clusters, wrap both in cling film and par-cook them separately in the microwave. Let cool.
Wrap the spinach in cling film and par-cook in the microwave. Refresh in cold running water. Squeeze out the excess water and cut into 3 cm long pieces.
Crush the tofu from Step 1 with a spoon. Crush any lumps in the sugar, and add it and the mentsuyu to the tofu. Mix well until the tofu mixture is smooth.
Add the cooled vegetables from Steps 2 and 3, and it's done.
Story Behind this Recipe
I love shira-ae, and I wanted to make it easily at home, so I used silken tofu which doesn't need a grinding bowl or a food processor to turn into a smooth paste, as well as all-purpose mentsuyu sauce which gets rid of any need for miso or sesame paste.
In order to reduce the amount of water, I use concentrated mentsuyu sauce. Start by draining the water from the tofu first. When the kitchen paper towels become soaked, change them.