Position rack in the center of the oven and heat the oven to 400°F. Line a rimmed baking sheet with parchment.
In a large bowl, whisk 1/4 cup of the olive oil with the mustard, Worcestershire sauce, caraway seeds, 1/2 tsp. of the salt, and about 15 grinds of pepper. Add Brussels sprouts, tossing to thoroughly distribute the mustard mixture. Spread the sprouts in an even layer on the baking sheet.
Roast until the cores of the sprouts are just barely tender and the leaves are browning and crisping a bit, 20 to 25 minutes (if your oven heat is uneven, rotate the pan midway through cooking).
Sprinkle the toasted walnuts, if using, over the sprouts just before serving.