In a medium saucepan, heat the olive oil over medium heat. Add the minced garlic and sauté until fragrant, about 1 minute.

Stir in the pumpkin puree, thyme, nutmeg, salt, and pepper. Mix well and cook for another 2-3 minutes until heated through.

In a separate bowl, toss the shredded cheeses with cornstarch to coat. This will help prevent clumping.

Gradually add the cheese mixture to the pumpkin mixture, stirring continuously until the cheese is fully melted and the fondue is smooth.

Transfer the fondue to a serving bowl or a fondue pot to keep it warm.

Serve with fresh bread cubes, apple slices, and assorted vegetables for dipping.