Izakaya Ramen Monji

Yes they boil all the noodles in the same thing

Nope, they do not

Ramen bowls are roughly $10 - $15.

The menu specifies ingredients and a green leaf icon indicates which dishes are available as vegetarian options. Moreover, the servers are trained to tell customers who ask which ingredients are gluten free. It is possible, for example, to order shirataki (白滝), which are noodles made from konnyaku (also known as yam noodles). But otherwise, I have seen nothing in terms of calories, grams of fat, etc. It isn't McDonald's... It is a real restaurant.