Preheat the oven to 350 degrees. Prepare a baking pan by lining it with parchment paper or a silicone mat.
In a medium bowl, whisk together the flour and the baking powder.
In the bowl of an electric mixer, mix the butter, until it is soft and fluffy. Add the sugar, lemon zest and salt, and mix in. Add the eggs one at a time, and mix until just incorporated.
Stir in the flour mixture until just combined, followed by the apricots and 1 cup of the chocolate chips.
Place the dough onto your prepared baking sheet and form it into a rectangular log, about 13x3 inches. Place in the oven and bake for about 35 minutes, or until the cookie log is golden brown. Let it cool for 30 minutes.
Transfer the cookie onto a cutting board. Using a serrated knife, cut on a slight diagonal in 1/2 inch slices. Return the cookies to the baking sheet, arranging them cut side down. Bake for 10-15 minutes, until the cut sides are golden. Transfer the cookies to a rack to cool completely.
Melt the remaining white chocolate in a double boiler (if you do not have one, bring a little water to a simmer in a small saucepan and place a heatproof bowl over it). Carefully transfer into a piping bag or ziploc bag. Drizzle generously over the cooled biscotti. Place in the refrigerator to firm for about 30 minutes.