In a medium saucepan, bring the broth to a simmer.
In a large heavy saucepan over low heat, melt the butter.
Stir in the onions, jalapenos and garlic and cook, stirring once or twice, for 5 minutes.
Add the rice, stir to coat well with butter, and cook 2 minutes.
Stir in 1 cup of the hot broth. Cook, stirring frequently, until the rice absorbs almost all the broth, about 5 minutes. Continue adding broth 1 cup at a time and stirring often between additions, until the rice has absorbed most of the broth and is tender and creamy, about 30 minutes total.
Stir 1/3 cup of the grated cheese into the risotto, cover, and let stand 1 minute.
Divide the risotto evenly between 6 plates and serve immediately, passing the remaining cheese and a peppermill at the table.