Coat two 15" x 10" x 1" jellyroll pans with cooking spray; line with wax paper, and coat wax paper with cooking spray. Set aside.
Beat eggs in a large bowl at medium-high speed of an electric mixer 5 minutes. Add water, beating at low speed until blended. Gradually add cake mix, beating at low speed until moistened. Beat mixture at medium-high speed 2 minutes. Fold in grated carrot.
Spread batter evenly in prepared pans (layers will be thin). Bake, one at a time or in separate ovens, at 350° on the middle rack 13 minutes or until each cake springs back when lightly touched in center.
Sift 1 1/2 tablespoons powdered sugar in a 15" x 10" rectangle on a cloth towel; repeat with 1 1/2 tablespoons sugar and a second towel. When cakes are done, immediately loosen from sides of pan, and turn each out onto a sugared towel. Peel off wax paper. Starting at narrow end, tightly roll up each cake and towel together; place, seam side down, on wire racks to cool completely.
Drain pineapple, reserving 1/4 cup syrup. Press pineapple between paper towels to remove excess moisture. Combine pineapple, cream cheese frosting, and 1/2 cup pecans; stir well.
Unroll cakes; brush each lightly with 2 tablespoons reserved pineapple syrup. Spread each cake with half of frosting mixture. Reroll cakes without towels; place, seam side down, on serving plates.
Cover and chill at least 1 hour. Dust cakes with additional powdered sugar before serving. Garnish, if desired.
Note: For spice cake mix, we used Duncan Hines.
Note: This recipe makes 2 cake rolls, so it's ideal for a make-ahead dessert for a crowd. Or give the second roll as a gift.