Cozy Mushroom Farrotto

Name: Cozy Mushroom Farrotto
Prep time: 20 min
Cook time: 1 h 5 min
Total time: 1 h 25 min
Cuisine: Italian
Ingredients: 3 tablespoons neutral oil (such as canola oil | divided); 1 pound assorted mushrooms*; Salt and black pepper; 2 tablespoons unsalted butter; 1 medium onion (finely diced); 3 cloves garlic (finely minced); 2 sprigs fresh thyme (or rosemary); 1 cup farro (semi-pearled | drained and rinsed); 3/4 cup dry white wine; 4 cups vegetable broth (preferably mushroom broth or bouillon); 1 teaspoon soy sauce (optional); 1/2 cup freshly grated parmigiano-reggiano cheese (plus more for serving); 1/4 cup minced fresh flat-leaf parsley; Olive oil (for serving)