For the pastry, combine the butter, flours and sugar in a food processor and pulse until well combined and resembles fresh breadcrumbs. Add egg yolk, mixing until well combined. Remove from the bowl and bring together with your hands and form into a flat disc. Cover and refrigerate for 20 minutes.
Roll dough onto a lightly floured surface and press into a 20cm fluted tart pan with removable base. The dough will be quite soft, so you can trim and press it together quite easily to fit the pan. Refrigerate for 20 minutes. Pre-heat oven to 200°C (180°C fan-forced).
Prick pastry base with a fork, line with baking paper and fill with blind baking weights or beans. Bake for 20 minutes, remove paper and weights and cook for a further 8-10 minutes until base is cooked through. Remove and allow to cool. Reduce oven temperature to 180°C (160°C fan-forced).
For the frangipane, place butter and sugar in a bowl and mix with electric beaters until pale and creamy. Add eggs one at a time, until well combined, then fold in the almond flour. Pour into the cooled pastry case. Press in the pear slices and sprinkle with almonds. Bake for 45-50 minutes or until cooked in the middle. Brush with apricot jam while still warm. Serve with cream or ice-cream.