Preheat olive oil in a deep skillet or pot over medium heat. Add chopped onion and sauté until translucent. Add ground beef sauté until no red meat can be seen, breaking the meat into very small pieces as it cooks.
Stir in dill, mint, salt, pepper, and the 1/4 cup of white wine or Vermouth.
When liquids resume a boil, add 1 cup of medium grain rice and 1/4 cup of boiling water. Stir to mix well and cook for about 20 minutes, stirring frequently to keep the mixture from sticking to the pan as the rice absorbs the liquid.
Remove pot from the heat and stir in cheeses until thoroughly mixed in.
