Heat vegetable broth in a medium pot until simmering.
Lower heat, whisk in miso paste until dissolved—don’t boil miso!
Add tofu and seaweed; cook gently for 5 minutes.
Stir in green onions, remove from heat, and keep warm.
Whisk cornstarch into 1/2 cup soy milk until smooth.
Heat remaining soy milk, coffee, and sugar in saucepan until hot.
Gradually whisk in cornstarch mix, stirring until pudding thickens (about 5 minutes).
Remove from heat, stir in vanilla, and cool slightly.
Serve soup warm, then finish with chilled coffee pudding.