Prep + Season: Preheat oven to 400°F (204°C). Remove pork (2) from packaging and pat very dry with paper towels — any surface moisture will prevent a good sear. Rub all over with Dijon mustard (1 teaspoon), then season generously with salt and pepper.
Sear the pork: Heat the oil and 1 tablespoon butter in a large ovenproof skillet over medium-high heat until the butter just begins to foam and the mixture is shimmering. Add the tenderloins and sear until a deep golden-brown crust forms on all sides, about 2–3 minutes per side. Adjust heat slightly if the butter starts to darken too quickly — you want steady browning, not scorching.
Add thyme + roast: Drop the fresh thyme sprigs (2-3 sprigs) into the hot pan and spoon the pan juices over them to infuse the flavor. Transfer skillet to the oven and roast 12–15 minutes, or until an instant-read thermometer registers 140°F.
Rest the pork: Transfer the tenderloins to a platter and loosely tent with foil. Let rest for 10 minutes — the temperature will rise to a perfect 145°F (63ºC), and the juices will redistribute for moist, tender slices. 👉 While the pork rests, start the sauce. Caramelize pears with layered shallots (sweet layer): In a separate skillet, melt 1 tablespoon butter over medium heat. Add half of the shallots (¼ cup) and cook 2–3 minutes until translucent and just turning golden. Add pears, sugar (1 teaspoon), pinch of salt, and optional cinnamon or pepper. Sauté, stirring occasionally, until pears are tender and deeply golden, about 8 minutes. Remove from heat and set aside.
Build pan sauce (savory layer): Return the pork skillet to medium heat, discard the thyme sprigs, and add 1 tablespoon butter. When melted, add the remaining shallots (¼ cup) and sauté until softened, 2–3 minutes. Stir in thyme leaves (1 teaspoon), then deglaze the pan with white wine (1/4 cup), scraping up all the browned bits. 👉 Cook until the liquid is syrupy and reduced to just a few tablespoons before moving on — this concentrates flavor and prevents a thin sauce. Reduce and build flavor: Stir in pear schnapps (1/4 cup) and simmer 1–2 minutes until slightly syrupy. Add cream (1 cup), pear nectar (1/3 cup), Dijon mustard (1/2 teaspoon), lemon juice (1 teaspoon), and (if using) chicken base (1 teaspoon). Simmer 5–7 minutes, stirring often, until the sauce thickens enough to coat the back of a spoon. Season with salt and pepper to taste.
Finish the sauce: Stir in the caramelized pears and swirl in 1 tablespoon cold butter off the heat for a silky finish.
Serve: Slice the rested pork into medallions. Arrange on a platter and spoon the warm pear-cream sauce generously over the top. Garnish with a few fresh thyme leaves if desired.