Preheat the oven to 400 degrees F (200 degrees C). Fit puff pastry into a 10-inch square tart pan with removable sides.

Place a pear half, cut-side down, onto a work surface. Place a chopstick above and below the pear half, so the pear is framed on the top and bottom. Thinly slice the pear half lengthwise, stopping when the knife hits the chopstick and leaving the bottom 1/4 inch of the pear intact. Repeat with the remaining pear halves.

Place hasselbacked pears in a bowl. Add white sugar and lemon juice and gently toss to coat; let pears stand for 5 minutes.

Mix cream cheese, confectioners' sugar, and vanilla extract together in a bowl; spread over puff pastry. Arrange hasselbacked pears over cream cheese layer, cutting some of the halves into quarters if needed to fit them in. Slightly fan out each pear and drizzle any accumulated juices from the pear bowl over pears. Sprinkle turbinado sugar over tart.

Bake in the preheated oven until crust is puffed and lightly browned and juices are bubbling, about 35 minutes. Cool tart for 15 minutes before slicing.