Put the flour in the bowl of a food processor with the 100g butter. Blitz until the mixture resembles fine breadcrumbs, then add 50g of the cheese, 1 tbsp of the thyme leaves, some freshly ground black pepper and 1 tsp salt. Blitz again briefly to combine. Add 2-3 tbsp cold water, and pulse again until it comes together into a dough. If you don’t have a food processor, do this in a bowl – rub the flour into the butter first, then stir in the remaining ingredients with a knife. Wrap and chill for at least 40 mins.
Meanwhile, heat the 25g butter and the olive oil in a large frying pan over a low-medium heat, and cook the onions with a pinch of salt for 40-50 mins, stirring often, until sticky, golden and very soft when pressed with the back of a spoon. If they start to catch, reduce the heat further and add a splash of water. Be patient, as they will take a while to caramelise, but keep your eye on the pan so they don’t burn.
Stir in the vinegar, sugar and the anchovies. Keep stirring until the vinegar has evaporated, and the anchovies have dissolved into the onions. Remove from the heat.
Heat the oven to 190C/170C fan/gas 5 and roll the pastry out onto a lightly floured work surface to a 3mm thickness. Use the pastry to line a 23cm tart tin (use the rolling pin to help you do this). Trim the edges so they’re just overhanging the sides. Patch the pastry with the offcuts, if needed. Scrunch up a sheet of baking parchment, then open it out again to line the pastry, and fill with baking beans. Bake for 15 mins, remove the parchment and beans, then bake for a further 5-8 mins, or until the pastry looks dry, without any raw spots.
Meanwhile, whisk the eggs, cream, remaining thyme and the rest of the cheese together with a pinch each of salt and black pepper. Stir in the caramelised onions. Trim the sides of the pastry using a serrated knife to neaten the edges. Pour the filling into the pastry case and tap the tin gently on the work surface to release any bubbles.
Bake the quiche for 25-30 mins on the middle shelf of the oven until lightly golden and set in the middle, with a slight wobble. Leave to cool in the tin for at least 15-20 mins, then slice. To make the salad, whisk the olive oil and vinegar together in a bowl, then toss in the remaining ingredients. Pile the salad on top of the quiche, or serve alongside. If you like, leave the quiche to cool completely, then chill before serving. Will keep in the fridge for up to three days.