Drain the tofu and wrap the tofu around a layer of paper towels. Press the tofu by placing the tofu block on a plate and weighing it down with a stack of plates. Let it sit for 15 to 20 minutes. Remove the towels and cut the tofu into small 1/4-inch cubes.
Heat 1 1/2 tablespoons of oil in a large pan. Add the minced ginger and garlic and cook for 1 minute. Then, add the cabbage, carrots, and a pinch of salt to the pan and cook for 3 to 4 minutes. Transfer the tofu and scallions to the pan and add another pinch of salt. Cook for another 2 to 3 minutes. Taste the filling. You want the the filling to be a smidgen saltier than you would normally prefer. The wonton wrappers will mellow out the saltiness of the filling.
Get your dumpling-making station set up. Transfer the filling into a large bowl. Take the wrappers out of the packaging. Have a small bowl filled with water, a large baking sheet, and 2 kitchen or linen towels ready. The wrappers and the dumplings dry out pretty quickly. Use one towel to cover the wrappers and another large towel to cover the finished dumplings.
Dip a finger into the bowl of water and wet 2 adjacent sides of the dumpling wrappers. Spoon about 2 teaspoons to 1 tablespoon of filling into the center of the wrapper. If you can fit more filling into the dumpling, great! Seal the wrapper on the diagonal (dry sides over the wet sides) so that you end up with a triangle shape. Press down on the sides to make sure that you have the dumpling properly sealed. You don't want the filling to release while they're cooking.
Lightly wet one of the base corners of the folded triangle, and fold the dumpling in half so that the other base corner overlaps the wet corner. Repeat until you have all the dumplings filled. If you need a visual, refer to the video or photos in the post for the folding technique.
Check the curry broth and see whether it's still warm enough for your liking. If not, heat it up over medium-low heat and keep it simmering on low as you cook the dumplings.
Bring a big pot of water to boil. Add about half of the dumplings into the boiling water and cook for 3 to 4 minutes. All the dumplings should float to the top. Transfer the cooked dumplings to a bowl and add the remaining dumplings into the hot water.
Ladle some of the curry broth into a bowl and serve with the dumplings. Top with chili oil and black sesame seeds, if you like.