Preheat the oven to 190°C and line a baking sheet with parchment paper.
In a large mixing bowl, combine the finely diced mushrooms, shredded tofu, shredded carrot, chopped spring onions, minced ginger, and minced garlic.
Add vegetable oil, soy sauce, rice vinegar, and cornstarch to the mixture and combine well.
Fill a shallow dish with warm water. Dip one sheet of rice paper into the water until it softens slightly.
Place a spoonful of the filling mixture onto the rice paper and fold the edges to form a dumpling.
Brush each dumpling with vegetable oil and place on the prepared baking sheet.
Bake in the preheated oven for 20-25 minutes or until the dumplings are crispy and golden brown.
While the dumplings are baking, prepare the dipping sauce by combining sugar, hot water, soy sauce, rice vinegar, chili oil, minced garlic, toasted sesame seeds, and sesame oil in a bowl.
Serve the baked rice paper dumplings hot with the dipping sauce. Garnish with sesame seeds if desired.
