Suvir Saran's Farro and Mushroom Burgers

Ingredients (13)

• 3/4 cup farro
• 1 pound red potatoes (about 3)
• 1 sprig fresh rosemary
• 1 sprig fresh thyme
• 6 tablespoons unsalted butter
• 1 teaspoon freshly ground black pepper
• 1 pound cremini mushroom caps, finely chopped
• 1 1/4 teaspoon kosher salt
• 5 to 8 tablespoons extra-virgin olive oil
• 3 shallots, finely chopped
• 1 tablespoon dry white wine, dry vermouth, or water
• 1/2 cup finely grated Parmigiano-Reggiano cheese
• 1 cup panko bread crumbs