On a lightly floured surface, roll the pie dough into a 14-inch round. Grease the bottom and sides of a 10-inch tart pan with a removable bottom using the softened butter. Lay the dough gently into the pan without stretching, then press it into the bottom and up the sides. Roll a rolling pin over the top edge to trim away excess dough. Chill the crust in the refrigerator while you prepare the filling.

For the poached peaches: In a medium saucepan, stir together 2 cups water, the 2 cups sugar, lemon zest, and lemon juice. Bring to a simmer over medium heat. Add the peach halves skin side up and cook until the skins begin to pucker 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 to cool slightly. Slip off and discard the skins. Reserve 2 tablespoons of the poaching liquid and discard the rest or strain and refrigerate it for another use.

Preheat the oven to 375 degrees F.

For the almond filling: In a medium bowl, use an electric mixer to beat the 6 tablespoons butter and 1/2 cup sugar on high speed until creamy. Beat in the eggs one at a time, mixing well after each addition. Beat in the almond flour and 1/2 teaspoon almond extract until smooth. Spread the filling evenly over the bottom of the chilled tart shell.

Thinly slice the peaches and arrange the slices in concentric circles over the filling. Drizzle the reserved 2 tablespoons of poaching liquid over the fruit.

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

For the glaze: Melt the peach preserves in a small saucepan over low heat, about 5 minutes, or combine the preserves with 1 tablespoon of water in a glass measuring cup and heat in the microwave for 30 seconds. Press the melted preserves through a fine-mesh strainer to remove any solids. Brush the warm strained preserves over the top of the cooled tart.

For the mascarpone topping: In a medium bowl, beat the mascarpone, heavy cream, powdered sugar, and 1/4 teaspoon almond extract with an electric mixer on high speed until soft peaks form. Spoon the whipped mascarpone over the tart and spread it gently, leaving some of the peach surface visible. Sprinkle the sliced toasted almonds over the cream. Serve at room temperature or lightly chilled.

Cover any leftover tart and keep it at room temperature for up to 1 day.