Preheat the oven to 400°F. Place the pork loin in a large roasting pan and rub it with 1 tablespoon olive oil, half the minced garlic, the thyme, salt, and pepper.
In a bowl, toss the carrots, parsnips, and potatoes with the remaining 2 tablespoons olive oil and the rest of the minced garlic. Spread the vegetables around the pork in the pan.
Roast for 45 to 55 minutes, or until the pork reaches 145°F in the thickest part and the vegetables are tender.
While the pork rests, make the reduction. Pour the apple cider into a saucepan, add the minced shallot, and bring to a simmer over medium heat. Cook until the liquid reduces by half, about 10 minutes.
Remove the pan from heat and stir in the butter until melted. Slice the pork and serve with the roasted vegetables and a drizzle of the warm reduction.