For the dippers: Preheat the oven to 400 degrees F.
Lay the carrots, potatoes and cauliflower on a rimmed baking sheet and drizzle with half the olive oil, some salt and pepper and 1 teaspoon caraway seeds. Toss to coat. Bake for 15 minutes. Remove from the oven and push the vegetables over to one side. Lay the green beans, bread cubes, salami and grapes on the empty side and drizzle those with the remaining olive oil, some salt and pepper and the remaining teaspoon caraway. Return to the oven and roast until starting to brown on the edges and the vegetables are tender, an additional 7 to 10 minutes. Serve hot or at room temperature with fondue.
For the fondue: Bring the white wine to a low simmer in a fondue pot. Toss the cheeses, cornstarch, mustard and nutmeg together in a large bowl. Add in handfuls to the simmering wine, whisking to melt before adding more. Continue to add until all of the cheese has melted and the fondue is thick and smooth, 2 to 3 minutes. Whisk in the kirsch and serve with the dippers.