Bring a large pot of water to a boil. Carefully add the napa cabbage leaves (making sure not to tear or rip the leaves) and cook for about 3-4 minutes until softened. Remove, gently pat dry with paper towel, and set aside.
Heat a large skillet over medium heat with 1 Tbsp olive oil. Add the ground chicken to the skillet, breaking it up, and cook until browned and no longer pink, about 2-3 mins. Add the garlic, ginger, and shallot and sauté until fragrant, about 1 min. Add the mushrooms and carrot and cook for 2–3 minutes until softened. Stir in soy sauce, oyster sauce, sesame oil, salt, and mix well.
Stir the corn starch slurry mixture as the starch tends to settle towards the bottom then add it to the filling. Cook for another 30–60 seconds until the mixture thickens slightly and holds together. Turn off the heat and let the filling cool slightly.
Lay a napa cabbage leaf flat, trim a small portion of the thick stem on the bottom, spoon about 1 Tbsp of filling near the base, then roll it up like a burrito, folding in the sides and rolling tightly. Repeat with remaining leaves and filling.
Heat another large skillet with a tiny bit of olive oil over medium heat. Add the cabbage rolls and pan-fry for 2–3 minutes per side until lightly golden and warmed through. Cook in batches as needed.
In a small bowl, mix together all the sweet soy sauce ingredients until the sugar is dissolved.
Transfer the cabbage rolls to a serving plate, drizzle with the sweet soy sauce, and top with sesame seeds, chopped green onions, and chili oil. Serve immediately.
