Deep-fry frozen tenderloins at 350 degrees F for 3 to 5 minutes. Remove from fryer; drain.

 

Place rice in sieve or colander and wash with cold running water until water runs clear. Drain well. Transfer to large saucepan. Add water to rice in saucepan. Cover. Bring to boil over high heat. Reduce heat to low and simmer for 15 minutes. Do not uncover.

 

While rice is cooking, combine next 4 ingredients in small saucepan. Heat over medium heat for 1 to 2 minutes, or until sugar has dissolved. Remove from heat; cool. Add cooled vinegar mixture to the rice slowly, with a slicing and tossing motion. 

 

Lay sheets flat on work surface. Portion rice 1/4" thick over lower two-thirds of each sheet, using 3/4 cup of rice. Lay chicken tenders horizontally, overlapping narrow ends, on lower third of rice. Use 2 tenders for each sheet. Roll in jelly roll fashion. Slice into 1" thick slices (8 slices per roll). Serve on a bed of 1 oz barbecue sauce and 1 oz pesto sauce spooned onto plate. Rolls may be assembled in advance, covered and refrigerated. Serve cold or reheat to serve warm.