Position racks in the top and bottom thirds of the oven and heat oven to 400°F Line two rimmed baking sheets with parchment.
In a large bowl, whisk 1/4 cup of olive oil with the mustard, Worcestershire, caraway seeds, 1/2 teaspoon salt and about 10 grinds of pepper.
Add the sprouts and toss to distribute the mustard mixture. Spread the sprouts in an even layer on the two baking sheets.
Roast until cores of the sprouts are just barely tender and the leaves are browning and crisping a bit, 20 to 25 minutes.
While the sprouts are roasting, make the topping. Line a plate with two layers of paper towels. Heat the remaining 1 tbsp of oil with the mutter in a medium skillet over medium-high heat. When the butter has stopped foaming add the breadcrumbs all at once; toss to coat with butter mixture.
Reduce heat to medium, add the walnuts and 1/4 tsp, salt and cook, stirring constantly until the crumbs are browned and slightly crisp and the nuts are golden, 4 to 6 minutes. Dump the breadcrumb mixture onto the paper towels to drain the excess fat.
Transfer the sprouts to a serving bowl and season to taste with salt and pepper if necessary. Sprinkle the crumbs over the sprouts just before serving.