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Peel the celery root and slice in not too thick slices. Use a cookie cutter to create perfect rounds of celery root, make sure they're about the same size as the apple.
Coarsely chop the walnuts and divide the cheese into not too thick slices and set aside.
Heat a grill pan on high heat and drizzle the celery slices with olive oil. Grill them on both sides until they're almost completely soft and then season them with pepper and salt. Pre-heat the oven to 180 degrees Celsius or 350 degrees Fahrenheit.
Remove the core from the apple with an apple corer and divide the apples into slices, same thickness as the celery root. Add 4 slices of celery on an oven tray.
Add a slice of apple with a bit of thyme leaves followed by a slice of goat's cheese. Then again celery, apple, thyme, goat's cheese and finish with celery and goat's cheese.
Add some more thyme sprigs in between the stacks.
Bake the stacks in the oven for about 15 minutes, the exact time depends on the thickness of the apple and celery root slices. Transfer the stacks to plates and finish with some more thyme leaves and chopped walnuts, serve immediately. Enjoy!