Cut kohlrabi into thin noodles using a spiralizer.
Heat a large skillet over medium heat. Add bacon and onion; brown until bacon is beginning to crisp and onion is caramelized but not burning, 10 to 12 minutes. Transfer to a small bowl, reserving 1 tablespoon bacon grease in the skillet. (If there is not enough bacon grease, add enough oil to make 1 tablespoon grease.)
Add kohlrabi to the skillet and season with salt. Cook over medium heat, stirring occasionally, until kohlrabi begins to wilt and soften, 12 to 14 minutes. Stir in butter until melted. Add bacon and onion mixture and stir in 1/2 of the Parmesan.
Serve immediately topped with remaining Parmesan and parsley.