Step 1 Line 4 x 2cm-deep, rectangular (5cm x 10.5cm) loose-based tart tins with pastry pieces, trimming to fit. Place tart tins in freezer for about 15 minutes, or until pastry is frozen. Preheat oven to 180°C.
Step 2 Place tart tins on a large baking tray. Line pastry cases with baking paper and top with ceramic pie weights (or uncooked rice). Bake cases for 8 minutes, or until edges are just golden. Remove weights and paper, then bake for 10 more minutes, or until pastry cases are light golden; leave to cool.
Step 3 Meanwhile, add cinnamon stick to 1 litre water in a small saucepan and bring to the boil. Add pear halves. Reduce heat to medium. Simmer pears for 10 minutes, or until tender, then remove from cooking liquid and leave to cool. Cut each pear half diagonally into thin slices, preserving fruit shape.
Step 4 Combine apricot conserve with 1 tablespoon boiling water in a small bowl. Brush bases of pastry cases with half of the conserve mixture. Place a sliced pear half in each pastry case; brush with remaining conserve mixture.
Step 5 Scatter pear tarts with flaked almonds (if using) and serve.