Preheat oven to 350 degrees F. Toss grapes with 2 tablespoons olive oil, thyme, and 1/4 teaspoon salt. Roast for 45-50 minutes, until skins are bursting and wrinkled.
Meanwhile, slice goat cheese into 1/4 inch thick round, and place in a container. Pour remaining olive oil on top and let sit while grapes roast.
When grapes are finished roasting, let cool for at least 10 minutes.
Then arrange cheese plate by placing goat cheese down, then grapes and thyme sprigs, chopped walnuts, and remaining salt. Pour some of the olive oil remaining in dish where the goat cheese was marinating on top of all ingredients. Serve with toasted bread.
To toast walnuts, spread them on a sheet pan and bake for 6-7 minutes, at 350 degrees F, until just fragrant. Remove them, and let cool - they'll continue to cook as they cool.