Wrap the tofu in a dishtowel and put a 125 gram / 4 ounce weight on top. Let the tofu sit this way for 1 hour. Change the dishtowel whenever it gets soaking wet. Drop the spinach leaves into 3 cups of boiling water and boil rapidly for a minute. Drain and rinse under cold water. Mince.
Combine the miso, sake, sugar, and dashi. Mix to form a smooth paste. Pour this paste into a small, heavy pot or cast iron skillet and set over a medium low flame. When the mixture begins to bubble, turn the flame to low. Stir and cook the mixture until it is as thick as applesauce. Remove from the fire. Add the spinach and sesame seeds. Mix.
Cut the tofu into rectangles that are no bigger than 6.5 x 2.5 x 2 centimeter (2 1/2 x 1 x 3/4 inch).
Heat a cast iron skillet or griddle over a medium flame until it is very hot. Lay the bean curd pieces in it. Cook each side 2-3 minutes or until lightly browned, turning the pieces over carefully with a spatula. Now smear one side of each piece generously with miso paste. Serve this way or place under a broiler, miso side up, until a few dark spots appear. Serve hot.