Farro can be cooked like risotto, following the same stir-and-absorb method. Serve this double- mushroom version as a vegetarian main course or as a side for a rich main, such as braised short ribs.
Add 6 cups water, the porcini, tomato paste, and thyme to a large saucepan and bring to a boil. Reduce to a steady simmer.
Meanwhile, heat the olive oil in a medium Dutch oven over medium-high heat until shimmering hot. Add the onion, carrots, and celery. Sprinkle with 1 tsp. salt and a few grinds pepper. Cook, stirring, until the vegetables become tender and browned, about 6 minutes.
Add the cremini mushrooms and farro, and cook, stirring, until the mushrooms start to soften, about 2 minutes.
Add the wine and cook, stirring, until it almost completely cooks off.
Reduce the heat to medium, add about 1/2 cup of the mushroom broth, and cook at a steady simmer, stirring frequently, until the broth almost completely cooks off, 2 to 3 minutes.
Continue cooking, stirring, and adding the broth until the farro is tender and all of the broth has been added, about 25 minutes.
Stir in the mozzarella and Grana Padano, and season with salt and pepper to taste. Serve immediately, sprinkled with more fresh thyme.