Preheat the oven to 200°C/fan180°C/gas 6 and line a large baking tray with baking paper. Grate the Parmesan on a medium grater into a bowl. Divide small heaps of the cheese on the baking sheet, spaced apart, to make 8 in total. Sprinkle the thyme over each cheese pile. Bake for 4-5 minutes, until melted, lacy and golden.
Remove and set aside for 1 minute to firm up a little. Lay each crisp on a rolling pin, to curve it slightly, then cool. Serve with the Campari cooler.