Bring a large pot of salted water to a boil for the potatoes. Salt the water like the sea (about 1–1.5% salt by weight if you measure) — this seasons the potatoes from the inside as they cook.

Trim any silver skin from the pork and pat the medallions dry with paper towels. Season both sides generously with salt and pepper. Drying the surface removes moisture so the meat sears instead of steams, producing a flavorful brown crust.

Add the new potatoes (whole if small, halved if larger) to the boiling water and cook until just tender when pierced with a paring knife, about 12–15 minutes depending on size. Undercooking slightly will help them hold together when smashed.

While the potatoes simmer, make the glaze: whisk together the honey, tamari and half the chopped thyme (reserve the rest for the potatoes), and the minced garlic in a small bowl. The acid and salt in tamari balance the honey’s sweetness; whisking up front ensures even glazing later.

Heat a large heavy skillet (cast-iron preferred) over medium-high heat until very hot. Add 2 tbsp olive oil and swirl. When oil is shimmering, sear the pork medallions in a single layer, about 2–3 minutes per side until deep golden brown. High-heat searing develops the Maillard crust, which adds umami and texture.

Reduce heat to medium, push the medallions to one side, pour the prepared glaze into the empty side of the pan and let it bubble for 30–45 seconds to warm through and concentrate. Spoon the glaze over the pork as it cooks 1–2 minutes more, turning once, until the internal temperature reaches 60°C (140°F) on an instant-read thermometer. Target 60°C because the pork will continue to rise during resting to the safe USDA recommended 63°C (145°F) with a 3-minute rest; this keeps it juicy and slightly pink in the center.

Transfer the pork to a cutting board, brush with any remaining glaze from the pan, and tent loosely with foil. Rest for 6–8 minutes. Resting allows juices to redistribute and firms the pork just enough for clean slicing.

Drain the potatoes and let them sit in the colander for 1–2 minutes to lose excess steam. Place them on a rimmed baking sheet, use the bottom of a sturdy glass or a potato masher to gently smash each potato to about 1–1.5 cm thick — you want some surface area to crisp, but not pulverized.

In a wide skillet over medium heat, melt the butter with the remaining 2 tbsp olive oil. When foaming subsides, add the smashed potatoes in a single layer, cut-side down. Sprinkle with half the remaining thyme, salt and pepper. Cook undisturbed 3–4 minutes until golden and crisp, then flip and crisp the other side 2–3 minutes. Browning the flat surfaces adds crunchy contrast to the soft interior.

While the potatoes crisp, steam the broccolini: place a steamer basket over a pot with 2–3 cm simmering water (don’t touch the water). Add broccolini, cover, and steam until bright green and tender-crisp, about 3–5 minutes. Steaming (rather than boiling) preserves color, nutrients and that pleasant snap.

If you like, toss the steamed broccolini with a squeeze of lemon and a drizzle of the remaining tablespoon of olive oil, plus a pinch of salt to brighten the flavors and cut the glaze’s sweetness.

Slice the rested pork medallions crosswise into 1–1.5 cm slices. Plate: place a few smashed potatoes, a cluster of broccolini, and fan the pork slices on top. Spoon any reserved glaze over the pork and finish with the remaining fresh thyme and a grind of black pepper. Serve immediately.