To make the pastry, put the flour, butter and feta in a food processor and pulse to a sandy texture. Add the egg yolk, pulse briefly, then add 1 tbsp chilled water and pulse again. Add another tbsp water and pulse again, then a third - the dough should start sticking together - then add the poppy seeds. Tip out the pastry onto a worktop and bring it together into a ball. Don’t overwork it - you want it to have a nice flaky texture. Wrap in baking paper and chill in the fridge for 1 hour.
For the topping, finely slice the tomatoes and lay flat on kitchen paper. Whizz the almonds and basil in a mini chopper until you have a bright green crumb (or grind together in a large pestle and mortar).
Heat the oven to 220°C/200°C fan/gas 7. When it’s rested, roll out the pastry on a lightly floured surface to a large 2-3mm thick oval (use a knife to trim and neaten the shape, if you need to). Carefully transfer the pastry to a large baking sheet lined with baking paper and prick all over with a fork. Scatter over the basil-flavoured almonds, leaving a 2cm border around the edge. Layer over the tomatoes, slightly overlapping them, then drizzle lightly with oil and season with salt flakes and freshly ground black pepper.
Fold the pastry border back over itself to create a rim, pinching it at 2cm intervals, then laying the pinches flat to create a gentle pleated pattern. Brush the pastry with egg wash, then bake the galette for 20 minutes. Turn the oven down to 180°C/160°C fan/gas 4 and bake for a further 20 minutes. Serve hot or cold, topped with shavings of feta, extra basil leaves and a drizzle of olive oil.