Line a tart pan with parchment paper. Preheat the oven to 400 degrees F (200 degrees C).

Combine butter and 1/2 cup plus 2 tablespoons sugar in a large bowl; beat using an electric mixer until smooth and creamy. Mix in almond flour. Add eggs 1 at a time and mix until well combined.

Line a tart pan with the puff pastry and prick with a fork all over.

Place chocolate in the top of a double boiler over simmering water. Stir frequently, scraping down the sides with a rubber spatula to avoid scorching, until melted, about 5 minutes. Cool slightly. Cover puff pastry with melted chocolate.

Carefully pour egg mixture on top of the chocolate on the puff pastry without mixing the 2 layers. Arrange pear slices on top of the tart.

Bake in the preheated oven until pastry has puffed up and is golden brown, 25 to 30 minutes.