Heat the olive oil in a large pot over medium heat. Add the onion, carrots, and celery. Cook for 5 minutes until the vegetables begin to soften.
Stir in the garlic and mushrooms. Cook for another 4 minutes until the mushrooms release their liquid and start to brown.
Add the farro, vegetable broth, diced tomatoes, thyme, and oregano. Bring the mixture to a boil.
Reduce the heat to low and simmer uncovered for 25 minutes, stirring occasionally, until the farro is tender.
Stir in the white beans and spinach. Cook for 3 more minutes until the beans are heated through and the spinach wilts.
Season with salt and black pepper to taste before serving.