Press the tofu to remove excess moisture, then crumble it into a bowl using your hands or a fork. If using dried shiitake mushrooms, soak them in boiling water for 15 minutes before dicing.

Heat sesame oil in a medium skillet or wok over medium-high heat until the oil shimmers. Add the scallions and garlic and sauté until fragrant, about 2 minutes.

Stir in the carrots and mushrooms and cook for another 2 minutes until they are tender and slightly softened.

Add the crumbled tofu, soy sauce, white pepper, salt, and five-spice powder. Cook for 2 minutes, then stir in the cornstarch. Continue cooking until the mixture thickens and begins to bind together. Transfer the filling to a bowl and let it cool for at least 5 minutes.

Place a small amount of filling in the center of a wonton wrapper. Moisten the edges with water and pleat or fold to seal tightly. Repeat with the remaining wrappers and filling.

Bring a large pot of water to a boil over high heat and add a pinch of salt. Reduce the heat to medium-high and add the wontons in batches. Boil for 1 to 2 minutes, stirring gently so they do not stick to the bottom.

Remove the wontons with a slotted spoon once they float to the top and the wrappers look translucent. Reserve a small amount of the cooking water to use for the sauce.

Whisk together the reserved cooking water (or vegetable broth), chili oil, soy sauce, rice vinegar, sugar, sesame seeds, and sesame oil in a small bowl. Pour the sauce over the warm wontons and serve immediately.