You need to use pears that are soft textured so they bake well. If theyu2019re hard, poach them till theyu2019re soft but firm. Let them cool. You can poach them with some honey, cinnamon and ginger or spices of your choice for better flavour, and then reduce the poaching liquid to make a sauce to serve with the tart.
Put the flours, powdered almonds, the baking powder and the sugar in the processor bowl and pulse a couple of times to mix well. Add the chilled butter pieces and run the processor till the mixture resembles bread crumbs. Add the egg, and process to mix it in. and everything comes together away from the sides. Do not over process. The dough will be a bit soft, almost sticky. Turn the dough out onto your counter. Bring it together into a ball.
Butter a 9" tart pan with a removable bottom. Lightly dust your fingers with flour and press the ball of dough into a round shape. Place this in the buttered part pan, and coating your fingers with flour as and when you need to, press the dough out into the pan and up the sides to form an even crust.
Arrange the 6 pear halves on the crust and press down slightly. Mix together the cinnamon powder and 1 tbsp of sugar and sprinkle evenly over the pears. Bake at 180C (350F) for about 45 to 55 minutes until the crust is golden brown. Let the tart cool.
Just before serving the tart, heat together the apricot jam and lime juice in a small pan and brush this over the tart. Slice and serve as is, or with ice cream or whipped cream.