In a food processor, pulse together the flour, powdered sugar, and salt until combined.
Add the cold, cubed butter and pulse until the mixture resembles coarse sand.
Add the egg and pulse just until a dough forms.
Shape into a disk, wrap tightly in plastic wrap, and chill in the refrigerator for at least 1 hour.
Roll the chilled dough out on a floured surface into a circle, then transfer it into a 9-inch tart pan.
Trim the edges, dock the bottom gently with a fork, and freeze for 20 minutes. Bake in a preheated oven at 180°C (350°F) for 15–20 minutes, until light golden brown. Let cool for 10 minutes.
In a large bowl, using an electric hand mixer, beat the room-temperature butter, sugar, and salt until smooth and creamy.
Add the eggs one at a time, mixing well after each addition.
Fold in the almond flour and a touch of all-purpose flour until homogeneous. Transfer the mixture to a piping bag.
Assemble the tart
Pipe the frangipane filling into the cooled tart crust in a spiral pattern, smoothing the top gently with an offset spatula. Sprinkle sliced almonds evenly across the surface.
Bake at 175°C (350°F) for 30–35 minutes, until the filling is puffed, golden, and set in the center. (Cover loosely with foil if the almonds brown too quickly. Cool completely before slicing.
Notes
Butter Temperature: Ensure your butter for the Pâte Sucrée crust is ice-cold before cutting and mixing to guarantee a flaky, tender texture.
Chill the Crust: Do not skip the 20-minute freezer rest for the shaped crust before baking. This prevents shrinkage and structural collapse.
Don't Overmix Frangipane: Beat the almond cream just until smooth to prevent incorporating excess air that causes uneven puffing or sinking.
Make-Ahead Option: The unbaked pastry dough can be refrigerated for up to 3 days or frozen for 1 month. The frangipane can be mixed 24 hours in advance and stored in the fridge.
Prevent Over-Browning: If the sliced almonds on top start browning too quickly during the last 10 minutes of baking, loosely cover the tart with aluminum foil.