Preheat the oven to 220°C (425°F). Arrange a rimmed baking sheet and line it with parchment or a light brushing of oil. High oven heat helps the roots caramelize quickly, concentrating sweetness and creating texture that contrasts with the silky mash.

Toss the carrots and parsnips with 1 tablespoon olive oil, 1/2 teaspoon salt and a few grinds of pepper. Spread in a single layer on the baking sheet (don’t crowd them). Roast for 25–30 minutes, turning once halfway, until golden at the edges and tender when pierced. Roasting at high heat encourages Maillard browning, developing the roasted, nutty flavors that will deepen the mash.

While the roots start roasting, bring a large pot of salted water to a boil. Add the Yukon Gold potatoes and simmer until tender, about 15–18 minutes depending on size. Cooking the potatoes in well-salted water seasons them through; Yukon Golds are naturally buttery and mash up creamy without heavy dairy.

Prepare the pork: pat the medallions dry with paper towels (this is crucial — moisture prevents a good sear). Season both sides lightly with salt and a generous grind of black pepper. Let them sit at room temperature while the potatoes boil (5–10 minutes) so they cook evenly.

Heat a large skillet (preferably stainless steel or cast-iron) over medium-high heat until just smoking. Add 1 tablespoon olive oil and swirl to coat. Sear the pork medallions in a single layer (work in two batches if needed) for 1.5–2 minutes per side until a deep golden crust forms. Searing develops the Maillard reaction — flavor and color — and the fond left on the pan will be the foundation for the sauce. You do not need to fully cook the center; we’ll finish in the sauce.

Transfer the seared medallions to a plate and tent with foil to rest. Lower the heat to medium and add the remaining 2 tablespoons olive oil to the skillet. Add the Dijon mustard and stir it into the oil briefly (15–20 seconds) to bloom its flavor; then pour in the apple cider, scraping the browned bits (fond) from the bottom of the pan with a wooden spoon. Deglazing dissolves those concentrated flavors into the liquid and forms the base of the sauce.

Bring the cider-mustard mixture to a simmer and add 1 teaspoon of the chopped thyme. Let it bubble gently for 4–6 minutes, reducing slightly so the sauce gains body and the raw-cider edge mellows. Taste and adjust seasoning — the sauce should sing of apple brightness and mustard tang.

Return the pork medallions to the skillet and spoon the sauce over them. Simmer gently for 3–4 minutes until the pork registers 62–65°C (144–149°F) at the thickest part for a slightly pink, juicier center, or 68°C (155°F) if you prefer fully cooked. Finishing in the sauce warms the meat through while allowing time for the flavors to marry; avoid overcooking or the medallions will dry out.

Drain the potatoes and return them to the hot pot. Add the roasted carrots and parsnips (reserving a few roasted pieces for garnish if you like), 2 teaspoons chopped thyme, a pinch of salt and pepper, and 1–2 tablespoons of the hot pan juices or a drizzle of olive oil. Mash until smooth but still textured — you want body from the roasted roots. Using hot liquid (pan juices) rather than cold milk keeps the mash hot and cohesive without diluting flavor.

Taste and adjust seasoning of both mash and sauce. If the cider sauce is too sharp, swirl in 1/2 teaspoon more Dijon or a small pat of butter (optional) to round it out. Spoon a generous bed of root mash onto each plate, top with 3–4 pork medallions, and finish with spooned cider-mustard sauce and a sprinkling of fresh thyme leaves and freshly cracked pepper.

Serve immediately. Resting the pork briefly before serving lets the juices redistribute so each bite is tender and juicy; finishing in the sauce ensures every slice is glossy and flavorful.