Roll out the pie dough into a 14-inch round. Lightly butter the bottom and sides of a 10-inch tart pan with a removable bottom. Drape the dough into the pan without stretching it, then gently press it into the bottom and up the sides. Trim the overhang by rolling a rolling pin across the top of the pan. Transfer the crust to the refrigerator while you make the filling.

For the poached peaches: In a medium saucepan, combine 2 cups water, the sugar, and the lemon zest and juice. Bring to a simmer over medium heat. Add the peach halves and cook until the skins start to wrinkle and the fruit is just tender when pierced with a knife, about 5 minutes. Use a slotted spoon to transfer the peaches to a plate and let cool slightly. Slip off and discard the skins. Measure out 2 tablespoons of the poaching liquid and set it aside; discard the rest or save it chilled for another use.

Preheat your oven to 375°F.

For the almond filling: In a medium bowl, beat the softened butter and sugar with an electric mixer on high speed until creamy. Beat in the eggs one at a time, mixing well after each addition. Beat in the almond flour and almond extract until smooth. Spread the filling evenly over the bottom of the chilled tart shell.

Slice the peaches thinly and arrange the slices in concentric circles over the filling. Drizzle the reserved poaching liquid over the fruit.

Bake the tart until the filling is set and golden brown and the crust is golden, about 40 to 45 minutes. Let cool to room temperature on a wire rack.

For the glaze: Warm the peach preserves in a small saucepan over low heat, about 5 minutes. Or heat in a microwave with 1 tablespoon of water for 30 seconds. Strain through a fine-mesh sieve to remove any solids. Brush the warm glaze over the top of the cooled tart.

For the topping: In a medium bowl, beat the mascarpone, heavy cream, powdered sugar, and almond extract with an electric mixer on high speed until soft peaks form. Spoon the whipped mascarpone over the tart. Scatter the toasted sliced almonds on top. Serve at room temperature or lightly chilled.

Keep any leftover tart covered at room temperature for up to 1 day.