Roast the beetroot: Preheat oven to 200°C (fan). Wrap the peeled beetroot in foil and roast for 40–50 minutes or until tender. Allow to cool, then slice into thin wedges or rounds.
Caramelise the onion: In a small pan over medium-low heat, cook the sliced onion in a drizzle of olive oil until soft and golden. Add a splash of balsamic glaze and cook for another 2–3 minutes until sticky and fragrant.
Sauté the mushrooms: In a separate pan, heat 1 tbsp olive oil. Add mushrooms and cook until golden and any moisture has evaporated. Season with salt, pepper, and herbs if using.
Make whipped feta: Reserve a small portion of feta for the assembly. Blend feta, lemon juice, olive oil, and black pepper in a food processor or with a stick blender until smooth and creamy.
Prepare the pastry: Roll the chilled olive oil pastry into a 30cm circle on baking paper. Transfer to a baking tray.
Assemble: Spread the whipped feta (except reserved spoonful) over the centre of the pastry, leaving a 4–5cm border. Layer the beetroot, mushrooms, and caramelised onion over the top.
Fold and bake: Fold the edges of the pastry over the filling, pleating gently. Brush the crust with egg or milk if using. Bake for 30–35 minutes or until the crust is golden and crisp.
Serve: Let the galette cool slightly. Sprinkle with feta and fresh herbs before slicing.