Preheat oven to 400°.
To prepare cake, coat a 15 x 10-inch jelly roll pan with cooking spray, and line with wax paper. Coat paper with cooking spray; set aside.
Lightly spoon flour into dry measuring cups, and level with a knife. Combine flour, baking powder, and salt, stirring with a whisk. Beat eggs in a large bowl with a mixer at high speed until pale and fluffy (about 4 minutes). Gradually add the granulated sugar, vanilla, rind, and almond extract, beating until thick (about 4 minutes). Sift half of flour mixture over egg mixture; fold in. Repeat procedure with the remaining flour mixture. Spoon batter into prepared pan; spread evenly.
Bake at 400° for 10 minutes or until cake springs back when touched lightly in center. Loosen cake from sides of pan; turn out onto a dish towel dusted with 2 tablespoons powdered sugar. Carefully peel off wax paper; cool 1 minute. Starting at narrow end, roll up the cake and towel together. Place, seam side down, on a wire rack; cool completely (about 1 hour). Unroll carefully; remove towel. Spread jam over cake, leaving a 1/2-inch border. Reroll cake, and place, seam side down, on a platter. Sprinkle with 2 tablespoons powdered sugar. Cut into 8 slices.
To prepare coulis, drain apricots in a colander over a bowl, reserving 1 tablespoon juice. Place the apricots, 1 tablespoon reserved juice, honey, and amaretto in a blender; process until smooth. Serve with cake. Garnish with berries.