Special Equipment: 14-inch rectangular tart pan
Heat oven to 350° F. Butter a 14-inch rectangular tart pan and set aside.
Combine the flour and baking powder in a medium bowl and set aside.
Cream the butter and 1/2 cup sugar at high speed in the large bowl of an electric mixer. Lower speed to medium, add the egg, and beat until incorporated. Gradually add the flour mixture until fully incorporated. The dough will be very soft. Push the dough into the pan with floured fingers to form an even crust. Arrange the pear halves, top to bottom, cut-side down. Sprinkle with the cinnamon and the remaining sugar. Bake until the crust is golden brown, about 45 minutes; let cool.
Heat the apricot jam and lemon juice in a small saucepan over medium-low heat, mixing until combined. Remove from heat and brush gently over the entire tart. Serve with the whipped cream, if desired.
Tip: If you don't have a rectangular tart pan, you can use a 10-inch round tart pan. The dessert can be made up to 2 days in advance, covered, and kept in the refrigerator.