Preheat the oven to 200°C/gas mark 6. Peel the beetroot and wrap each individually in foil. Roast in the oven for 1 hour until tender. Leave to cool, then cut them into quarters or eighths depending on their size.
Place the flour, salt and butter in a food processor and whizz until it resembles breadcrumbs. Add 1 egg along with 1 tbsp of water and pulse again once or twice, until just starting to come together. Tip the dough out on to a floured surface and knead briefly until it comes together. Flatten into a disk and wrap in clingfilm. Chill for at least 30 minutes.
Once the pastry has chilled, roll it out until it’s about 3-5mm thick. Using a 10-11cm cutter, cut out 12 rounds, re-rolling the pastry as necessary. Divide the beetroot between the rounds, placing it in the centre and leaving about a 2cm rim. Top with the goat's cheese and hazelnuts. Crimp up the edges of the pastry to form mini galettes. Beat the remaining egg and brush it over the top of the galettes.
Bake in the oven for 20-25 minutes, until golden. Sprinkle over the thyme, then leave to cool on a wire rack.