Preheat the oven to 350 degrees F.
In a small bowl, stir together the flour, baking powder, salt, and rosemary. Set aside.
Using an electric mixer and a large mixing bowl, beat butter and sugar together until light and fluffy, about 4 minutes. Add the eggs, 1 at a time, incorporating each egg fully before adding the next. Add the vanilla. and gently stir in the flour mixture until just combined. Stir in currants.
Cut dough in half and shape into 2 logs. They should be about a 12-inches long; and 1-inch thick.
Bake until just starting to brown at the edges, about 35 minutes. Let cool for a few minutes on the baking sheets. While the biscotti logs are still warm, cut each log into 1/2-inch wide slices on the diagonal. Place the slices back on the baking sheet (using 2 baking sheets if necessary to fit all the slices). Bake for 7 to 8 minutes. Remove the baking sheets from the oven. Turn the biscotti over and bake for an additional 7 to 8 minutes, until the biscotti are crisp.
Let the biscotti cool for a few minutes on the baking sheet(s). Serve when cooled to room temperature, or store in an airtight container for up to 2 weeks.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.