Heat oven to 450 degrees. Prepare the squash: In a large bowl, mix together olive oil, sugar, cinnamon, salt, pepper and cayenne. Add squash and toss well to coat with the spiced oil. Lay the squash pieces out flat on one or two rimmed baking sheets.
Roast squash until the bottoms are golden, 10 to 15 minutes. Carefully turn the pieces over and continue to roast until tender, another 10 to 20 minutes.
Meanwhile, make the farro: In a medium pot, bring the apple cider, 2 cups water and the salt to a simmer. Add farro and simmer until water is absorbed and the farro is tender, 20 to 30 minutes. If the liquid evaporates before the farro is done, add a little more water. Or, if there’s still liquid in the pot when the farro is done, drain it.
In a large bowl, whisk together vinegar, garlic and pepper. Whisk in olive oil. Add farro and toss well, adding more oil or salt, or both, if needed.
To serve, spoon the farro on a platter and top with the squash, feta, mint or arugula, or both, and a drizzle of olive oil.
