Preheat an oven to 450°F (230°C).
Season the beef with salt and pepper. Place on a baking rack set in a shallow roasting pan.
In a small bowl, stir together 2 tsp. of the paprika, 1 tsp. of the caraway seeds, 1/2 tsp. of the marjoram, the mustard and cayenne. Stir in 1 Tbs. of the olive oil, then rub the mixture all over the beef. Oil a large baking pan and add the brussels sprouts, halved shallots, the 1 Tbs. soy sauce, plus the remaining 2 1/2 Tbs. olive oil, 1 tsp. caraway seeds and 1 tsp. marjoram. Stir to coat.
Roast the beef and vegetables until an instant-read thermometer inserted into the thickest part of the beef registers 125°F (52°C) for very rare to rare, about 20 minutes, or until done to your liking. Roast the vegetables until tender and browned, about 25 minutes. Transfer the beef to a warmed platter, cover loosely with aluminum foil and let rest for 15 minutes.
Spoon 1 Tbs. of the fat from the roasting pan into a saucepan and set over medium heat (discard the remaining fat). Add the minced shallot to the saucepan and sauté until it begins to soften, about 1 minute. Add the vermouth to the roasting pan, set it over medium-high heat and bring to a boil, stirring to scrape up the browned bits from the pan bottom. Pour the mixture into the saucepan and boil until syrupy, about 3 minutes, then add the broth, the remaining 1/4 tsp. paprika and the 2 tsp. soy sauce. Boil the sauce until syrupy, about 5 minutes.
Remove the pan from the heat and pour in any juices from the platter. Whisk in the butter and the remaining 1/2 tsp. marjoram. Season with salt and pepper. Slice the beef and arrange on a warmed platter with the vegetables. Serve immediately with the sauce. Serves 4 to 6.
Adapted from Williams-Sonoma Healthy Dish of the Day, by Kate McMillan