Preheat the oven to 425 convection. Line a baking sheet with parchment paper.
In a medium pot, add the farro and enough water to cover by 2 inches. Season generously with salt. Bring to a boil, then reduce the heat to medium-low to maintain a rapid simmer for 20-25 minutes (see note on farro). Drain completely, then transfer back to the dry pot. Spread the farro out and up the edges to allow the steam to come off and cool down a bit.
To the baking sheet, add the mushrooms, carrots, oil, and salt. Toss to coat well, then spread out into an even layer. Bake for 20-25 minutes or until the veggies are tender and browned in spots.
Meanwhile, to a jar with a tight fitting lid, add the miso and lemon. Use a fork to mix/mash the miso into the lemon to get rid of any big lumps. Add the remaining ingredients and shake vigorously to combine.
To the warm farro, add the scallions and about half of the dressing and toss to coat. Add the veggies and remaining dressing and toss to combine.
Serve topped with toasted nuts and black pepper.