Line 2 rimless baking sheets with parchment paper or grease; set aside.
In large bowl, beat in eggs, milk and almond extract. In separate bowl, whisk together flour, baking powder and salt; stir into butter mixture. Stir in nuts and apricots.
On lightly floured surface, form into four 2-inch wide logs. Place, 3 inches apart, on prepared pans. Bake in top and bottom thirds of 350°F oven, rotating and switching pans halfway through, until light golden and firm, about 22 minutes. Let cool on pans for 10 minutes.
Transfer logs to cutting board. Using chef’s knife, cut diagonally into ½ inch wide slices. Stand slices upright, ½ inch apart, on prepared pans; bake in top and bottom thirds of oven, rotating and switching pans halfway through, until dry, about 30 minutes. Transfer to rack; let cool.
Dip half of each cookie into chocolate; return to rack and let set. (Make ahead: Layer between waxed paper in airtight container and store for up to 5 days or freeze for up to 3 weeks.) Makes about 48 cookies.