Preparation

• Position racks in the top and bottom thirds of the oven and heat the oven to 400°F. Line two rimmed baking sheets 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 10 grinds of pepper. Add the Brussels sprouts and toss to thoroughly distribute the mustard mixture. Spread the sprouts in an even layer on the two baking sheets.
• 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 pans midway through cooking).
• While the sprouts are roasting, make the topping: Line a plate with two layers of paper towel. Heat the remaining 1 Tbs. oil with the butter in a medium (10-inch) skillet over medium-high heat. When the butter has stopped foaming, add the breadcrumbs all at once; toss to coat with the fat. Reduce the heat to medium, add the walnuts and the remaining 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. (The crumbs will start to sound “scratchy” as they get crisp.) 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.

Make Ahead Tips

You can fry the crumb topping up to 2 hours before serving.