For brioche, combine flour, sugar and yeast in an electric mixer fitted with a dough hook. Whisk eggs and milk in a jug, then add to flour mixture and knead until well combined. With the motor running, add butter in batches, combining each addition well before adding the next, then knead until dough is smooth and elastic (7-8 minutes). Transfer to a lightly buttered bowl, cover loosely with a clean tea towel and set aside to rest in a warm place until doubled in size (1-2 hours).
Thinly slice pear halves lengthways, holding them together to retain the shape. Whisk crème fraîche, maple syrup and egg yolk in a bowl.
On a lightly floured surface, roll out the dough to a 35cm round. Fold 2cm of the edge inwards to form a border, then spread crème fraîche mixture within the border and arrange pear halves on top. Cover loosely with plastic wrap and set aside to rise (30 minutes). Meanwhile, preheat oven to 180C, then bake tart until golden and custard has set (25-30 minutes). Serve warm or at room temperature. It’s best eaten the day it’s made.