Heat the olive oil in a large pot over medium heat. Add the onion and cook for 3 minutes until it softens.
Stir in the garlic and mushrooms. Cook for 5 minutes, stirring now and then, until the mushrooms release their liquid and start to brown.
Add the farro, carrots, thyme, and vegetable broth. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 25 minutes until the farro is tender but still has some chew.
Stir in the spinach and cook for 2 minutes until it wilts. Season with salt and black pepper.
Ladle into bowls and top each serving with fresh parsley.