Cook andouille sausage in heavy small skillet over medium heat until browned and cooked through, about 5 minutes. Drain off fat; transfer sausage to cutting board and slice into 1/2 inch slices, cut each slice in half. Transfer slices to small bowl. Add parsley; stir to combine. Cool.
Working with one date at a time, cut slit along top of date. Gently pry open date and remove pit, leaving pocket. Stuff pocket with 1/2 slice of andouille. Wrap 1 bacon piece around each date, overlapping ends slightly; fasten ends with toothpick.
Heat oil in medium skillet over medium heat. Add dates, toothpick-side down, and cook without moving until bacon browns, about 5 minutes per side. Continue to cook until bacon is brown on all sides, turning dates occasionally, about 6 minutes longer. Transfer to paper towels to drain. Remove toothpicks. Serve warm.