- Heat oil in a sauté pan set over medium-high heat until it simmers. Season loins with salt and pepper and sear for 2 minutes on each side.
- Reduce heat to medium and add garlic and thyme to the pan. Start the process of cooking and basting the loins, turning them over and over, first on one side, then the other, as well as on both ends, tilting the pan slightly to scoop up oil.
- Continue turning and basting for about 7 minutes, until a cake tester inserted in the center of the loin and pressed feels warm, for medium-rare. Transfer loins to a cutting board to rest for 5 minutes.
- In a heavy saucepan set over medium-high heat, heat oil until it shimmers. Add meat scraps, distributing evenly over pan’s bottom, and cook undisturbed for 2 minutes, until well seared. Turn over and sear for 2−3 minutes more, until well browned.
- Stir in onions, celery, carrots, and garlic and cook, stirring occasionally, for 3−4 minutes, until golden.
- Add wine and scrape any brown bits from bottom of pan with a spatula. Continue to cook until most of the wine has evaporated, about 2 minutes.
- Stir in demi-glace, rosemary, bay leaf, and thyme. Bring to a simmer and cook for 12−15 minutes, skimming often to remove impurities and fat that rise to the surface. Strain through a fine-mesh sieve into a measuring cup and reserve for jus. Discard solids.
- Cook the butternut squash juice, squash, and salt in a saucepan set over medium-high heat until the squash is completely soft, about 20−25 minutes.
- Transfer to a food processor and purée until smooth.
- Using a rubber spatula, press the purée into a bowl through a fine-mesh sieve. Keep warm until ready to plate.
- Heat 1 tablespoon butter in a small saucepan over medium-high heat until it bubbles.
- Add shallots and let them sweat for 1 minute, until translucent.
- Stir in reserved lamb sauce and bring to a boil.
- Whisk in remaining butter, thyme, salt, and pepper. Keep warm while assembling the dish.
- In a small bowl, mix yogurt with spices.
- Set aside.
- Slice loins crosswise into 12 even slices.
- Divide the squash purée evenly among 6 deep-welled soup plates or pasta bowls.
- Overlap two slices of meat partially over purée. Spoon jus over the meat.
- Garnish with winter-spiced yogurt and toasted pepitas.