- Make the farro: Soak farro in 3 quarts of water for at least 4 hours, preferably overnight, then drain. In a medium pan, sweat onions with olive oil, then add farro and cook until lightly toasted. Add vegetable stock and bring to a boil. Reduce to a simmer and cook farro until al dente, about 30 to 45 minutes.
- Make the carrot puree: In a large pot, combine carrots, herb sachet, and stock and bring to a boil. Reduce to a simmer and cook until carrots are extremely tender and most liquid has evaporated. Remove and discard sachet. Puree carrots and remaining liquid in a blender until smooth.
- Roast the carrots: Preheat oven to 425 degrees. Toss carrots with enough canola oil to coat. In a cast-iron skillet over high heat, sear carrots until they start to brown. Finish cooking in oven until tender, about 15 minutes. Season to taste with salt.
- To assemble: In a large pot over medium-high heat, combine cooked farro and puree. Add butter, parsley, and parmesan, stirring constantly until incorporated. Transfer to serving platter or bowl and top with roasted carrots and more freshly grated parmesan.