Toast farro in a saucepan over medium heat until browned and nutty smelling, shaking the pan occasionally, about 4-5 minutes. Cover the farro with water (at least an inch over the farro) and add kosher salt to the water. Bring the farro to a boil and cook until tender but still chewy, 20-25 minutes. Drain the farro into the fine mesh strainer.
While the farro is cooking, pour the olive oil into a skillet and heat on medium high until shimmery. Add the cauliflower and saute, turning frequently, until crisp tender and browned on all sides, 5-6 minutes. Add the red onion and continue to saute for 2-3 minutes more. The cauliflower should be tender and the red onion should be soft with just a little bite left.
Mix together the dressing ingredients in a bowl until well blended.
Take the warm farro, cauliflower, and red onion and toss them with the dressing. Transfer the salad to a serving bowl. Top with the parmesan and parsley.