Drain the tofu and wrap in paper towels to absorb excess water. Puree in a food processor until smooth, then transfer to a bowl and set aside.
Bring a large pot of salted water to a boil. Fill a bowl with ice water. Cook the spinach in the boiling water until wilted, about 2 minutes, then drain and plunge it into the ice water.
Drain and squeeze out the excess water.
Toast the sesame seeds in a skillet over medium-low heat, tossing, until golden, about 3 minutes. Cool, then grind in a spice grinder. Stir the ground seeds, sugar, mirin, soy sauce and spinach into the tofu. Season with salt.
