Rinse and dry the peaches, cut them in half through the stem and remove the pits. Spread the 3/4 cup sugar in the bottom of the sauté pan, drizzle the lemon juice all over and fit in all the peach halves, cut side down, on top of the sugar.

Set the pan over medium heat and, without disturbing the contents, let the sugar dissolve in the juices released by the peaches. Raise the heat and bring this syrup to a boil, partially cover the pan, and cook the peaches in place for about 5 minutes, then turn them over and cook for a couple of minutes. Turn them over again to cook the skin side for 2 minutes.

Keep cooking and turning the peaches until they’re tender and glistening with the syrup they’ve absorbed, about 15 minutes or more, depending on ripeness. Cover the pan if the peaches seem hard; but otherwise cook uncovered. Keep the syrup bubbling and thickening, but don’t let it burn. Turn off the heat and let the peaches cool in syrup while you prepare the crust dough.

Put the almonds and sugar in the food processor bowl and process, and cocoa and blend with the almond powder. Drop in the egg white and process until incorporated. Scrape down the sides of the bowl, add the butter and process. Clean the sides again process once more to form a stiff, smooth and somewhat sticky dough.

Butter and flour the tart pan. Scrape all of the dough into the pan bottom. Moisten your fingers with water and press the dough, spreading it over the pan bottom in an even layer, with a rim of dough up against the fluted side ring. Blot up any moisture on the dough—from your wet fingers—with a sheet of paper towel.

Arrange a rack in the center of the oven, with a baking stone if you have one, and heat to 375°.

Spread the apricot jam in an even layer on the dough. Cut the cooled peach halves in two, so you have 16 or 20 wedge shaped fruit pieces, and place them in a flower-petal pattern, or other neat arrangement, completely filling the crust. Spoon some of the remaining peach syrup all over the fruit.

Set the tart on a cookie sheet or a sheet of heavy-duty foil (to catch the juices) and bake for 45 minutes or until the peaches are nicely caramelized and the crust is deeply browned. Cool briefly on a wire rack and separate the side ring from the crust before any caramelized juices are set.

While the peaches are still warm, drizzle over the last of the peach syrup, top with a scoop of vanilla ice cream. Serve right away, as the ice cream melts. A dollop of whipped cream or crème fraîche are other creamy choices I like.