Make the crust: Add the flour, powdered sugar, and a pinch of salt to the bowl of a food processor. Add the cold butter cubes and begin pulsing, 10–15 times, until the butter is fully incorporated into the flour.
Add the egg to the food processor and pulse just until a dough begins to form. Place the dough onto a work surface and knead it lightly, just to bring it together. Wrap in plastic and chill for 30 minutes.
Make the filling: Add the softened butter, granulated sugar, and salt to a medium bowl. Combine the mixture with an electric hand mixer, gradually increasing the speed from low to medium-high. Beat until fluffy, then add each egg, 1 at a time, scraping the bottom and sides of the bowl between each addition. Lastly, add the almond flour and all-purpose flour and combine on low speed until homogenous.
Arrange a rack in the lower third of the oven. Preheat the oven to 375°F (190°C).
Assemble the tart: Remove the tart crust from fridge and gently roll out to roughly a 12-inch round on a floured work surface. Transfer the dough to a 9-inch tart pan, then top with the filling, spreading it as evenly as possible.
Arrange the pears in a spiral pattern on top of the filling. Brush the entire surface with the melted butter, then sprinkle the granulated sugar over the pears.
Bake, rotating halfway through, for 50–55 minutes, or until the crust is browned and the center of the tart is no longer jiggly. Let cool completely before slicing.