In a large saucepan over medium heat, melt half the butter. When it begins to foam, cook the onions, stirring, until tender, 6-8 minutes.
Add the stock, Bijol, rice and salt and bring to a boil. Continue cooking until most of the liquid has been absorbed, 10-15 minutes, and small craters form on top of the rice.
Cover and simmer over low hear without stirring until all the stock has been absorbed, 10-15 minutes. Just before 3 - the parmesan cheese and stir to blend, using 2 forks.
Serving, add the remaining butter, cut into small peices, add the parmesan cheese and stir to blend, using 2 forks.