In a food processor add the flour, sugar, and salt. Pulse a few times to combine.
Add the butter and pulse until butter is the size of small peas.
In a small bowl whisk together the egg yolk and the water.
With the processor running drizzle the egg mixture into the flour until the pastry comes together.
Turn out onto plastic wrap, form into a disc, and refrigerate while you make the frangipane.
Clean out the food processor and add the sliced almond, sugar, and salt. Process until the almonds are finely ground.
Add the egg and the vanilla and almond extracts. Mix until well-combined.
Drizzle in the melted butter and pulse until mixed.
Set aside.
Next, roll out your pastry until it is about 13 inches in diameter and 1/8 inch thick.
Carefully drape it into an 11-inch tart pan with a removable bottom. Press into the sides and pinch off any excess.
Pierce the pastry all over with a fork to prevent bubbles while baking.
Freeze the tart shell while you preheat the oven to 375 degrees F.
Place the tart shell on the middle rack and bake for 15 minutes, or until just set. Then remove to a cooling rack. (I’ve found that if the crust is frozen first, it doesn’t tend to shrink..I don’t bother with pie weights).
Pour the frangipane into the still warm tart shell. Spread with a rubber spatula to even out the mixture.
Arrange the peach slices in 2 rings, or in whatever design you prefer.
Finally, sprinkle the entire tart with the additional 2 tablespoons of sugar.
Bake for 45-50 minutes or until the frangipane is puffed, set, and golden brown.
Cool on a cooling rack until it’s still warm to the touch, but can be handled.
Optional- dust with powdered sugar just before serving.