Melt butter in a large skillet over medium-high heat; add onion, and sauté 5 minutes. Add saffron, and sauté 1 minute.
Add rice, and cook, stirring constantly, 2 minutes. Reduce heat to medium; add vermouth and 2 cups broth. Cook, stirring constantly, until liquid is absorbed.
Repeat procedure with remaining broth, 1/2 cup at a time. (Cooking time is 30 to 45 minutes.)
Remove from heat, stir in cheese and pistachios.
*1 cup chicken broth may be substituted for vermouth.