Brussels sprouts are available already shredded in many supermarkets, but if you want to DIY, use your sharpest knife or a mandoline or pass them through the feed tube of a food processor fitted with the slicing attachment.
Combine 2 tablespoons vinegar, 1 teaspoon oil, garlic and 1/4 teaspoon each salt and pepper in a sealable plastic bag. Add steak, seal the bag and shake to coat. Place in a dish and set aside to marinate for 30 minutes (or refrigerate for up to 1 day).
Meanwhile, whisk the remaining 2 tablespoons vinegar, maple syrup, 1/2 teaspoon Dijon mustard and 1/4 teaspoon each salt and pepper in a large bowl. Whisk in the remaining 3 tablespoons oil. Add Brussels sprouts and toss to coat. Set aside.
Position rack in upper third of oven; preheat broiler to high. Line a baking sheet with foil.
Place potatoes in a medium saucepan. Add water to cover by 1 inch. Bring to a boil, cover and cook until tender, about 12 minutes. Drain, return to the pan and cover to keep warm.
Remove the steak from the marinade (discard the marinade) and place on the prepared pan. Broil, flipping once, about 8 minutes for medium-rare (135°F). Transfer the steak to a clean cutting board and let rest for 10 minutes.
While the steak rests, mash the potatoes with buttermilk, whole-grain mustard and the remaining 1/2 teaspoon each salt and Dijon mustard and 1/4 teaspoon pepper. Stir in 2 tablespoons chives.
Add figs, hazelnuts and the remaining 2 tablespoons chives to the reserved Brussels sprouts. Gently toss to combine.
Slice the steak against the grain and serve with the slaw and potatoes.
Marinate steak and refrigerate slaw (Steps 1-2) for up to 1 day. Let the steak stand at room temperature for 30 minutes before broiling.