To prepare the pork, mix dijon and mayo in a small bowl, then add minced garlic, rosemary, thyme, and 1 teaspoon of salt. Rub this mixture onto the pork rack, then refrigerate it for 6 hours. Before cooking, let the pork come to room temperature on the counter for 30 minutes.
To prepare the vegetables, preheat the oven to 425°F. Melt 2 tbsp of butter and set it aside. Roughly chop the carrots, turnips, parsnips, and onion, then toss them in a large bowl with 2 tbsp of the melted butter and season with 1/2 teaspoon of salt.
In a hot roasting pan over medium heat, add the remaining butter and coat the pan. Sear the pork with the fat side down until it's golden, which takes 3 to 5 minutes. Use tongs to sear the sides of the pork as well. Then, remove the roasting pan from the heat and set the pork aside.
To roast the rack of pork, place the prepared vegetables in the roasting pan and position the pork on top. Roast it in the oven at 425°F for 1 to 1.5 hours until the internal temperature reaches 145°F. Remove it from the oven and cover with foil. Let the roast rest for 20 minutes, then carefully slice between the bones and serve.