Wrap the block of tofu in 2 layers of paper towels and lay on a plate. Invert a second plate on top of the tofu and weigh down with a 28-ounce can. Leave for 20 minutes then cut the tofu into 1/4 to 1/2-inch cubes.
Heat the dashi in a 4-quart saucepan over medium-high heat. When the dashi reaches 100 degrees F on an instant-read thermometer, ladle 1 cup into a small bowl. Add the miso, and whisk until smooth.
Bring the remaining dashi to a bare simmer, approximately 10 minutes. Add the miso mixture and whisk to combine. Return to a slight simmer, being careful not to boil the mixture. Add the tofu and scallions and cook for another minute or until heated through. Remove from the heat, ladle into soup bowls and serve immediately.