1 1/2 to 2 teaspoons anise seeds, optional
10 tablespoons unsalted butter, sliced, at room temperature (1 1/4 sticks)
3/4 cup confectioners’ sugar
1 large egg
1 teaspoon pure vanilla extract
3/4 teaspoon fine salt
1 3/4 cups all-purpose flour
1 1/2 cups sliced almonds, with skin, plus 1/4 cup for top
6 tablespoons unsalted butter, sliced and at room temperature
1 cup confectioners’ sugar
1/2 teaspoon ground cinnamon
1 large egg
3/4 pound firm-ripe Italian, prune or Angeleno plums (about 10), pitted and halved or quartered
If using the anise seeds, lightly toast them in skillet over medium heat until aromatic, 2 minutes. Grind in a spice mill or mortar and pestle until fine.
Combine the butter and sugar in a food processor until creamy. Add the egg, anise seed if using, vanilla and salt and pulse to combine. (This may look rough and curdy, but don’t worry, it all comes back together.) Add about half of the flour and pulse quickly 3 to 4 times to incorporate. Scrape down the edges of the processor and add the remaining flour. Pulse just enough to make a coarse, crumbly dough.
Press dough into the bottom and up the sides of a 9-inch springform pan to form a thin, even layer, using waxed paper to smooth. Freeze crust while you prepare the filling.
Pulse 1 1/4 cup almonds in a food processor until very finely ground (take care not to overprocess the nuts or they can get oily). Transfer nuts to a bowl. In the same processor, combine the butter and sugar until smooth. Add the cinnamon and continue to pulse until evenly combined. Scrape down the sides of the bowl and pulse in the egg. Add the reserved almonds and pulse until just blended.
Arrange the plums cut side down, over the crust. Spread the filling on top and smooth with a small offset spatula. Sprinkle with the remaining almonds and place in the freezer for 30 minutes.
Preheat oven to 350 degrees F. Bake pie until the filling puffs and is golden but still slightly soft in the center, 1 hour 15 minutes for a glass bottomed pan, or 1 hour 30 minutes for an aluminum pan. If the crust begins to overbrown, cover the pie with foil during the last 15 minutes of cooking. When pie is done, turn off the oven and prop door open. Cool pie in the oven for 15 minutes, then transfer to a rack to cool completely.
Serve at room temperature with ice cream or lightly sweetened whipped cream.