Chop pecan halves into small pebble-sized pieces. Peel, trim, and cut carrots into 1/4" diagonal slices. Cut sunchokes into 1/2" dice. Mix liquid egg and brown sugar in a small bowl.

Add carrots and sunchokes to prepared baking sheet. Toss with 2 tsp. olive oil and season with 1/2 tsp. salt, 1/4 tsp. pepper, and half the red pepper flakes (to taste - red pepper flakes are spicy!). Roast on lower rack of oven 18-20 minutes, or until tender and lightly caramelized. Remove from oven and toss with sun-dried tomatoes.

While vegetables roast, rinse pork tenderloin and pat dry. On a separate cutting board, cut pork tenderloin into 1" thick medallions. Season each piece with a pinch of salt and pepper. Heat 1 tsp. olive oil in a medium oven-safe pan over medium-high heat. Add medallions to hot pan and sear 4-5 minutes, or until well-browned. Flip medallions and remove pan from heat (medallions will finish cooking later).

Spread egg-brown sugar mixture on top of pork medallions and sprinkle with pecans. Place pan on upper oven rack and finish cooking 6-8 minutes, or until pork reaches a minimum internal temperature of 145 degrees. Using an oven mitt or dry dish towel, remove pan from oven and remove medallions to a plate.

Place pan in which pork was cooked over medium-high heat (no need to wipe clean). Place a towel over handle as a reminder that it's still hot from oven. Add sherry wine and bring to a simmer. Reduce by half, about 2 minutes of simmering, and add demi-glace. Simmer 30 seconds, or until demi-glace is fully incorporated. Season with remaining red pepper flakes (to taste) and a pinch of salt.

Place a serving of carrot-sunchoke hash on plate. Serve crusted medallions in front along with pan sauce.