Preheat the oven to 350°. Spread the walnuts on a rimmed baking sheet and toast for 8 minutes, or until lightly browned.
Meanwhile, in a large saucepan, combine the sugar, port, pepper and bay leaf and bring to a boil. Cook over moderate heat, stirring occasionally, until slightly thickened, 3 to 4 minutes. Discard the bay leaf.
Add the walnuts to the saucepan, stirring to evenly coat them. Using a slotted spoon, drain the nuts very well. Line a baking sheet with parchment paper and spread the walnuts on it in a single layer. Bake for 12 minutes, stirring once, or until the nuts are mostly dry; let cool. Separate any nuts that stick together.
Meanwhile, simmer the syrup over low heat until it is thick enough to coat the back of a spoon, about 3 minutes.
Set the Stilton on a serving platter and place the walnuts in a separate bowl. Drizzle the port syrup over the cheese and serve with the nuts.
The nuts can be stored in an airtight container for up to 1 day. The port syrup can be refrigerated for up to 1 day; rewarm before serving.