The trick here is to make the broth first, then have the noodles and tempura done at exactly the same time. If the tempura sits for too long, it will get soggy, if the noodles sit for too long, they will stick together.
Prep the Chanterelles by cleaning them thoroughly. With a small brush and paper towels. Add them to a bowl along with the onions and green beans.
Boil some water for the noodles. Get a wire rack ready for the tempura by covering it with a layer of paper towels. Make sure you have some ice cold water on hand and that the bowl your going to mix the batter in along with the flour is nice and cold (I put them in the freezer for 10 minutes).
In a cast iron or other heavy bottomed pan, add about 1" of oil. Heat the oil until it reaches 340 degrees.
Add the flour to the vegetables and toss to coat evenly. Add the cold club soda and quickly mix until a batter forms, but do not over-mix or your batter with get tough.
Put a mound of the vegetables and batter onto a spatula and then use another one to push the mound into the oil being careful not to splash. Repeat with the rest of the batter and then fry until crisp, flipping the tempura over at least once.