Preheat oven to 375 degree F. Grease and flour a 15x10x1-inch baking pan. Set aside. Stir together the flour, baking powder, salt, and apple pie spice; set aside.
Drain apricots, reserving 1/3 cup of the syrup. Finely chop the apricots. Reserve 1/2 cup of the chopped apricots for the filling. Combine remaining chopped apricots, reserved apricot syrup, and the 2 tablespoons granulated sugar in a small sauepan. Bring apricot mixture to boiling; reduce heat. Cook and stir over low heat about 4 minutes or until thickened, stirring and mashing with a spoon. Remove from heat; cool to room temperature.
Beat eggs in a medium mixing bowl with an electric mixer on high speed for 5 minutes. Gradually beat in the 1/2 cup granulated sugar and apricot mixture. Gently fold flour mixture into egg mixture. Spread batter in prepared pan. Sprinkle with nuts.
Bake in preheated oven for 10 to 12 minutes or until wooden toothpick inserted near center comes out clean. Turn cake out onto a towel sprinkled with powdered sugar. Starting at a short side, roll up cake and towel together; cool.
Combine cream cheese, butter, and vanilla in a small mixing bowl. Beat mixture with an electric mixer on medium-high speed until fluffy. Beat in powdered sugar. Stir in the reserved 1/2 cup chopped apricots.
Unroll cake and spread with cream cheese mixture. Reroll without towel; cover and chill for at least 2 hours or up to 24 hours. Transfer cake roll to cake server. If desired, garnish with fresh apricot wedges and rosemary sprig. Makes 10 servings.