COMBINE cookie mix, butter and egg in medium bowl until soft dough forms. Divide dough in half. Add cocoa and milk to half of dough with wooden spoon until evenly distributed. Divide both halves in half again to make 4 parts. Roll each part between sheets of wax paper into 10 x 8-inch rectangles. Place flat layers of dough with wax paper in bewteen on cookie sheet. Chill 15 minutes.
COOK preserves and flour in small saucepan over medium heat, stirring constantly, until bubbly. Remove from heat. Stir in walnuts. Let cool. Remove one sheet of wax paper from sheets of dough. Spread half of preserves mixture evenly onto a chocolate layer. Place one light layer down over the preserves, aligning corners of doughs. Remove wax paper from light layer. Allow dough to soften slightly, about 2 to 3 minutes. Beginning on long side, roll up dough to make a rounded log, making sure the first roll in the center is tight. Roll wax paper around log. Repeat with remaining 2 sheets of dough. Freeze 1 hour.
HEAT oven to 375°F. Line cookie sheet with parchment paper. Cut logs into 1/4-inch slices. Place on prepared cookie sheet. Bake 10 to 12 minutes or just until lightly browned. Cool on cookie sheet 2 minutes. Transfer to wire rack to cool completely.
TIP Keep second log in freezer until ready to bake. Return to freezer as needed to make slicing easier.