In a small saucepan over low heat, melt the chocolate and shortening together, stirring until smooth. Remove from the heat and let cool for about 20 minutes.

In a mixing bowl, beat the eggs and granulated sugar with an electric mixer on medium speed for 2 to 3 minutes, until fluffy. Mix in the vanilla, then add the cooled chocolate mixture and beat until combined.

In a separate bowl, whisk the flour, baking powder and salt. Add the dry ingredients to the chocolate mixture and stir until fully incorporated.

Cover the dough and chill for at least 3 hours, or until firm enough to roll. Overnight chilling works well.

Preheat the oven to 375 degrees. Line a cookie sheet with parchment paper or lightly grease it. Place the powdered sugar in a shallow bowl. Shape the chilled dough into 1-inch balls, roll each ball in the sugar until coated, and place them 2 inches apart on the prepared baking sheet.

Bake for 10 minutes, or until the edges are set. Cool on a wire rack.