In a small bowl, whisk together the soy sauce, vegetarian oyster sauce, brown sugar, and chile powder.
Add the tofu to a medium bowl and drizzle with 1 tablespoon of the sauce. Gently toss to coat. Reserve the rest of the sauce.
Using your hands, break up the sheets of noodles into individual noodles. Set aside.
Heat 2 tablespoons of oil in a large nonstick wok or skillet over high heat, swirling the pan to coat. Working in batches, add the tofu to the pan in a single layer and cook for 1-2 minutes on each side, until browned. Flip and brown on the other side, 1-2 minutes more. Remove from the pan and set aside.
Add the remaining tablespoon of canola oil to the pan. Add the shallot to the pan and cook until tender and lightly browned, about 2 minutes. Add the garlic and water and cook for 30 seconds, until fragrant. Add the Chinese broccoli and cook, tossing occasionally, until crispy and tender, 2-3 minutes. Add the reserved rice noodles, tofu, and sauce and toss to combine. Cook until the noodles are warmed through and coated in the sauce, 1-2 minutes.
Push the noodles to one side of the pan and pour the eggs into the empty space. Cook for 30 seconds, stirring constantly, until the eggs are scrambled. Toss to incorporate the eggs into the rest of the dish.