Toss the quartered apricots gently with 3 tablespoons sugar and set aside to macerate for about 1 hour.

With a small knife, cut the green almonds along the crease, then twist to open. Pop out the kernel inside, and using the knife and your fingers, peel away the white skin to reveal an even whiter kernel. Collect all the green almonds in a bowl and discard all the scraps. Cut the almonds into slivers and set aside, covered with a damp towel, until ready to serve.

Stir together 2¼ cups sugar and 1½ cups water in a medium-size nonreactive saucepan. Split the piece of vanilla bean lengthwise and scrape out the seeds into the saucepan, reserving the pods for another use. Bring the mixture to a full boil, stirring frequently to dissolve the sugar and break up the bits of vanilla seeds.

Reduce the heat to a simmer, add the apricots, and poach them in the syrup for about 5 minutes, until very tender when pierced with the tip of a sharp knife.

Remove from the syrup and let cool. Divide the apricots among 4 dessert plates, spoon a few tablespoons of the vanilla syrup over each serving, and sprinkle the slivered green almonds on top. Serve alone or atop ice cream or fresh ricotta cheese.