For the pastry, put flour, sugar, baking powder and salt into a food processor and pulse to combine.
Add butter and pulse again until mixture resembles a fine powder.
Add eggs one at a time while continuing to pulse then scrape dough from the sides and continue pulsing until well incorporated.
Dough will have the texture of wet sand and will start coming together in clumps.
Shape dough into a disk, cover and chill until firm, about 1 hour.
Meanwhile, for the frangipane, put almond paste, sugar and 1 of the eggs into the food processor and purée until smooth.
Add butter, zest and vanilla and continue mixing until well combined.
Mix in flour and baking powder then add remaining egg and continue mixing until smooth and well incorporated.
Transfer frangipane to a medium bowl, cover and chill for at least 30 minutes.
Preheat the oven to 350°F. On a lightly floured surface, roll out pastry into a (13-inch) circle.
Transfer to an (11- to 12-inch) tart pan with a removable bottom, pressing pastry into bottom and sides of pan.
With the rolling pin, roll over the top of the pan to cut off excess dough then prick bottom and sides all over with a fork.
Spread frangipane mixture evenly over pastry.
Starting in the middle, arrange pears in a spiral pattern on top, pressing them down lightly and leaving some room between pear slices for frangipane to puff up.
Arrange tart pan on a baking sheet and bake until pastry is golden brown and frangipane is set in the center and golden, about 45 minutes.
Remove from oven, set aside to let cool for 15 minutes then carefully remove outer ring of pan and transfer tart to a serving plate. Serve warm or at room temperature.