I think the interesting thing about the chopped salad dressing is that it is sweet and sharp at the same time. I am not a master taster, but I tried the following and I thought it was pretty close to Portillo's dressing:

Poppyseed Dressing
Dry Mustard

All I did was add Poppyseed dressing to my salad. Then I sprinkled dry mustard on top of the dressing before mixing it all up. Then I tasted it and kept adding dry mustard until it had the right sharpness.