Remove leaves from cauliflower head, core, and cut into even, bite-sized florets. Trim ends off green beans. Peel and halve shallot. Slice into thin strips (julienne). Stem and mince thyme. Rinse pork tenderloin, pat dry, and season all sides with ½ tsp. salt and ¼ tsp. pepper.
Place cauliflower on prepared baking sheet. Drizzle with 2 tsp. olive oil and BBQ rub. Toss to coat and spread into a single layer, leaving room on one side to add pork tenderloin later. Bake 7 minutes and remove from oven (cauliflower will finish cooking later).
Apple-Glazed Pork Tenderloin with BBQ-rubbed cauliflower, caramelized shallots, and green beans
While cauliflower cooks, place a large non-stick pan over medium-high heat. Add 2 tsp. olive oil and pork tenderloin to hot pan. Sear on two sides, 2-3 minutes per side, or until each side is lightly browned. Remove pan from burner and transfer pork to baking sheet after cauliflower roasts 7 minutes. Roast an additional 8-10 minutes, or until cauliflower is tender and browned, and pork reaches a minimum internal temperature of 145 degrees. Remove from oven and let pork rest 3-5 minutes. Reserve pan (no need to wipe clean).
While pork cooks, return pan used to cook pork to medium heat. Add 1 tsp. olive oil and shallots to hot pan. Cook, stirring occasionally, 4-8 minutes, or until tender and caramelized. Transfer half the caramelized shallots to a plate. Combine cornstarch and apple juice in a small bowl and add mixture to pan with remaining shallots. Bring to a boil while stirring. Reduce heat to a simmer and cook 4-7 minutes, or until just thinner than honey. Season with ¼ tsp. salt, a pinch of pepper, and thyme. Remove from burner. Brush 1 Tbsp. sauce over resting pork tenderloin.
Place a medium pan over medium-high heat. Add 1 tsp. olive oil and green beans to hot pan. Cook 3 minutes, or until green beans are lightly browned and bright green. Add remaining caramelized shallots and ¼ tsp. salt. Cook 1-2 minutes, or until green beans are tender. Remove from burner.
Slice pork tenderloin into ½” thick slices. Place cauliflower and green beans on plate. Add sliced pork and spoon remaining sauce around pork.