Heat the oven. Preheat oven to 425°F and line a sheet pan with parchment paper.
Make the wonton strips. Cut the wonton wrappers into ½" wide strips. Add them to a bowl and toss with 1 teaspoon of oil. Spread them in a single layer on the baking sheet and bake for 6-7 minutes until golden brown and crisp. Remove them from the baking sheet and let them cool.
Heat the baking sheet. Remove the parchment paper from the baking sheet and return the baking sheet to the hot oven until you are ready to cook the brussels sprouts.
Roast the brussels sprouts. Add the brussels sprouts to a large bowl and toss them with 3 teaspoons of oil plus the salt and pepper. Spread them out in a single layer on the preheated baking sheet. Bake for 15 minutes then remove from oven and add the garlic and shallots. Stir to mix everything together. Return the baking sheet to the oven and roast for an additional 10 minutes or until the brussels are very browned and crisp.
Make the dressing. Add the honey, rice wine vinegar, tamari and sesame oil to a small bowl or mason jar. Mix to combine. Add the avocado oil, salt and pepper and mix again until all the ingredients are incorporated.
Assemble the salad. After the brussels are cooked, add them to a mixing bowl. Add the cabbage, carrots and cilantro. Toss to combine then add the dressing and toss again. Top with wonton strips and serve.