Wash and dry all produce. Peel Yukon Gold and sweet potatoes, then cut into 1/2-inch cubes. Cut any larger broccoli florets into bite-sized pieces. Roughly chop pecans. Pick 1 tsp thyme leaves from stems; reserve remaining sprigs. Pat pork dry with a paper towel, then season all over with salt, pepper, and autumn spice.

Place both potatoes in a medium pot with enough salted water to cover by 1 inch. Bring to a boil and cook until easily pierced by a knife, about 15 minutes. Drain well, then return to pot. Meanwhile, place pecans in a large pan and place over medium-high heat. Cook, tossing frequently, until toasted, 3-5 minutes. Transfer to a plate to cool.

Heat a large drizzle of oil in same pan over medium-high heat. Add pork and cook to desired doneness, 4-6 minutes per side. Set aside to rest on a plate. Place broccoli and a large splash of water in a large, microwave-safe bowl. Cover with plastic wrap and poke a few holes in wrap.

Microwave broccoli on high until tender, about 5 minutes. Thoroughly drain, then add 2 TBSP butter to bowl and toss to melt. Season with salt and pepper. Sprinkle with pecans. Place pot with drained potatoes over low heat. Cook one minute to evaporate excess water. Mash with a potato masher or fork until smooth, then stir in sour cream. Season generously with salt and pepper.

Rinse out pan used for pork and dry well, then place over medium-low heat. Add 2 TBSP butter and reserved thyme sprigs. Swirl pan or stir until butter melts, about 1 minute. Stir in demi-glace and maple syrup. Let simmer until slightly reduced, 1-2 minutes. (TIP: Lower heat if sauce bubbles aggressively.) Stir in any juices released by pork. Season with salt and pepper. Discard thyme sprigs.

Divide potatoes and broccoli between plates. Arrange pork on top of potatoes, then drizzle with sauce from pan. Sprinkle with thyme leaves and serve.