In a hot non-stick pan add in the mushrooms and cook until golden brown. Keep them moving to stop them from burning. When they are golden brown add in tamari sauce and thyme and stir until well coated. Remove from heat and place to the side until needed. In a large saucepan over medium heat, soften the onion in 2 tbsp of olive oil for 10 mins being careful not to brown the onions. Add the rice and cook for 1 minute, stirring to coat well.
Add the white wine and reduce until almost dry. Add the broth, 1 cup at a time, stirring frequently until the liquid is completely absorbed before adding more broth. Cook for 20 minutes or until the rice is firm to the bite but not raw. Add broth, as needed.
Take off the heat and add the butter & cheese. Stir until the texture is very creamy.
Add in the mushrooms and peas. Adjust the seasoning.
Serve in warm bowls and sprinkle with a little Parmesan cheese.