Fill a 13- x 9-inch pan with water. Cover top of pan with self-sealing plastic wrap. Place 2 strips of tape about 1⁄2 inch apart on the plastic wrap 1⁄2 inch from inside edge on each short side of pan. Using the paring knife, evenly cut Xs, smaller than the diameter of the carrots, in between strips of tape on each side. Fit carrots into Xs; secure with tape, if necessary.
Place pan on level rack in freezer, and freeze at least 24 hours. Remove plastic wrap, carrots, and, if necessary, tape. Run tap water over ice block to remove from pan. The frozen carrots will be soft and easy to dig out of the ice with a small spoon, if necessary. Place your choice of flowers in ice cavities.