1 Slice the tomatoes to 5mm (¼in) thick. Put them in a colander set over a large bowl and sprinkle over the salt. Set aside for 1 hour to draw out the juices.
2 If you have an oven-style air fryer, line a baking sheet with parchment paper. If using the basket kind, cut two pieces of parchment paper to fit the baskets, with an overhang of 5cm (2in) to help lift the galettes (or use silicone liners).
3 To make the pastry, tip the flour, butter and salt into a food processor and blitz to fine breadcrumbs. Add the egg and pulse to a soft dough – if the dough seems dry, add ½ teaspoon of cold water at a time until it comes together.
4 Knead the pastry briefly, pat into a round, and roll it out on a lightly floured work surface. Before the pastry is fully rolled out, transfer it to the prepared baking sheet and continue rolling out to a rectangle approximately 28x24cm. If making two smaller galettes, make the bases slightly smaller than the basket and liner so the steam can escape. This will prevent soggy bottoms.
5 Add half the cheese, arrange the tomatoes in an even layer, then sprinkle with thyme and the remaining cheese, leaving a border of about 5cm (2in) around the edge. Season with salt and pepper.
6 Brush the pastry border with egg wash, then fold the border up so it slightly overlaps the filling. Brush with more egg wash.
7 Preheat the air fryer to 160°C. Bake for 45–50 minutes for the large galette, 30–35 minutes for the smaller ones. The pastry should be golden and crisp, the tomatoes soft and browning. Remove the parchment paper and allow the base to crisp up for the last 5–10 minutes. Leave to stand for 5–10 minutes.
8 Serve warm, garnished with fresh herbs, with a side salad.
ADAPTATION: Switch the pastry for a gluten-free version.