Preheat oven to 300°F (150°C) and set oven rack to middle position.

Butter an 8x8-inch glass baking dish.

In a bowl using an electric mixer, cream together the softened butter, 1/2 cup confectioners' sugar, and vanilla until light and fluffy (about 5 minutes).

Add the grated lemon zest, lemon juice (if using), and poppy seeds to the creamed mixture.

Mix until just combined.

In a separate small bowl, mix together the all-purpose flour and salt.

Add the flour mixture to the creamed mixture.

Mix just until combined.

Press the dough mixture evenly into the prepared baking pan.

Bake for about 30-35 minutes, or until the edges are pale golden brown.

Let the shortbread cool in the pan on a wire rack for about 10 minutes.

Cut the shortbread into 24 bars while still in the pan.

Let the bars cool completely in the pan.

Sprinkle the cooled bars with confectioners' sugar.