Combine broth and water in a medium saucepan over medium heat. Bring to a simmer.
Heat oil in a Dutch oven over medium-high. Add tomatoes; cook 4 to 5 minutes, stirring occasionally, until blistered. Reduce heat to medium and add shallots, garlic, and mushrooms; cook 2 to 3 minutes. Add thyme, salt, black pepper, and farro; cook 2 minutes, stirring often. Add white wine, and bring to a boil. Reduce heat to medium; simmer 8 minutes or until liquid is reduced by half, stirring frequently.
Add broth mixture in 1-cup increments, stirring occasionally, cooking until the liquid is almost completely absorbed before adding the next increment, about 45 minutes total. Remove pan from heat; stir in Parmesan. Divide farrotto evenly among 6 shallow bowls; sprinkle with additional thyme and Parmesan cheese, if desired