Whisk the cornstarch with water in the bottom of a saucepan.
Add the brown sugar, black pepper, mushroom powder, garlic, and tamari to the pan and bring to a boil over medium heat, stirring occasionally. Reduce to low heat and cook for 2 minutes until the sauce thickens. Remove from heat and set aside.
Heat the olive oil in a large skillet over medium-high heat. After 90 seconds, when the oil is hot, add the tofu and cook for 6-7 minutes, stirring occasionally, until lightly browned.
Add the onion and garlic and continue to sauté for 3 minutes until the onion becomes fragrant.
Stir in the carrot, napa cabbage, vegan shrimp paste, vegetarian oyster sauce, and water. Cook for 2 minutes, stirring frequently, until the cabbage and carrots wilt. Remove from the heat and let the filling cool.
Place a lumpia wrapper on a clean surface. Lay 1 lettuce leaf and a generous pinch of jicama in the center of the wrapper. Spoon a portion of the cooked filling on top, followed by cilantro leaves.
Fold the bottom of the wrapper up over the filling, then fold in the sides and roll tightly. Repeat with the remaining wrappers and filling.
Serve the lumpia with the sauce, crushed peanuts, and chives on top of them.