Begin by rinsing the farro under cold water to remove any impurities. Drain well.
In a medium saucepan, bring the vegetable broth and water to a simmer over medium heat, then reduce to low to keep warm.
Heat the olive oil in a large, heavy-bottomed pan over medium heat. Add the chopped onion and sauté until translucent, about 3-4 minutes.
Stir in the minced garlic and cook for an additional minute until fragrant.
Add the sliced wild mushrooms to the pan, sautéing until they are tender and have released their moisture, around 5-7 minutes.
Stir in the farro, coating it with the oil and toasting it slightly for about 2 minutes.
Pour in the white wine and let it simmer until the liquid is mostly absorbed.
Begin adding the warm broth mixture, one ladle at a time, stirring constantly. Allow the liquid to be absorbed before adding more.
Continue to add the broth, stirring frequently, until the farro is creamy and al dente, which should take about 30 minutes.
Once the farro is cooked, remove from heat and stir in the grated Parmesan cheese. Season with salt and black pepper to taste.
Garnish with fresh thyme sprigs and serve immediately.