In a small bowl combine all the sauce ingredients. Mix well.
Heat vegetable oil in a large skillet under high heat. Once skillet is heated, add broccoli and stir fry for a minute or so until slightly softened. Add carrots and cook until they often as well, ~30 seconds. Remove and set aside.
Add more vegetable oil to skillet if needed. Heat on high heat. Once skillet is heated, add chicken. Once chicken is fully cooked, remove chicken and set aside. (See Note 1)
Add more vegetable oil to skillet if needed. Heat on high heat. Once skillet is heated, add minced garlic and sliced onions. Once they are fragrant (do not brown or burn), add sauce and 1 1/2-2 cups of chicken broth.
Bring to a boil then lower to medium high heat. Add three ramen noodle squares to skillet (they should be partially submerged in sauce). Ramen noodles will slowly soften. Use a spatula to gently press on noodle and submerge noodles into the sauce. Flip noodles over once they are slightly softened. Use spatula to separate them as soon as you are able to. Then coat all the noodles in sauce (I find that it is easier to do this using tongs).
Noodles should soften and absorb most of the liquid, and still be slightly saucy. Once noodles are softened, lower to medium heat and add cooked broccoli florets, cooked chicken and shredded carrots back into the skillet. Toss and combine everything in sauce (use tongs). Add more chicken broth if noodles are too dry.
Stir/cook for another minute or so. Remove from heat once everything is cooked.
Serve and enjoy!