Preheat the oven to 200°C.
Blend the flour, salt, butter, and sugar in a food processor until the mixture looks like breadcrumbs.
Gradually add the egg and water mixture until a dough forms.
Roll the dough between two sheets of baking paper into a 25cm circle and trim edges.
Heat sugar and water in an ovenproof frying pan over low heat until dissolved into a syrup.
Increase heat and simmer without stirring for 4-5 minutes until the mixture caramelizes.
Remove from heat and stir in 40g of butter until melted and thick.
Place apricot halves cut-side down into the butterscotch.
Cover with the pastry circle, tuck in the edges, prick with a fork, dot with remaining butter, and sprinkle with sugar.
Bake for 25-30 minutes until golden-brown and bubbling.
Cool for five minutes, then invert the tart onto a serving plate.
Serve warm or cold with cream or ice cream.