Preheat oven to 400°F. Prepare a large rimmed sheet pan with parchment paper and set aside.
Pulse almond paste and 3 tablespoons sugar in processor until finely chopped, about 6 to 8 pulses. Add cream cheese, whipped ricotta, egg yolk, and vanilla and blend until filling is smooth.
Unroll pie crust on parchment lined baking sheet. Using a ruler and a sharp knife, lightly score marks 1 1/2 inches in from the edge of the crust all the way around, so as to roughly leave a 1 1/2-inch plain border.
* if using licorice sugar, sprinkle 1/2 teaspoon on crust now
Spread filling over crust just to border marks you made.
Arrange apricot half fans atop the filling.
Fold dough border up over edge of filling.
Brush exposed apricots with warm jam. Sprinkle with remaining 1 1/2 teaspoons sugar.
Bake crostata until crust is golden brown and apricots are tender and slightly browned, about 40 to 45 minutes.
Sprinkle with crushed anisette cookies if using. Serve warm or at room temperature.