Cook brisket according to package directions (leave fat on, trim after it is cooked).
Meanwhile, add radish dressing ingredients to a blender or food processor. Blend until smooth. Store in refrigerator.
When ready to serve, remove brisket from slow cooker and scrape fat off. Cut across the grain into 1/2" strips. Transfer corned beef to a plate and cover tightly with foil while you prepare the potatoes and pitas.
Strain potatoes from the slow cooker and reserve 1/4 cup of the slow cooker spiced water. Add potatoes to a large bowl (peel first if desired) and mash with 1/2 cup Parmesan cheese and the 1/4 cup reserved slow cooker water. Cover with foil.
Toast pitas by heating a drizzle of olive oil in a skillet over medium heat. Cook approximately 1 minute per side, or until warmed and golden.
Assemble pitas by layering mashed potatoes, corned beef, cabbage then drizzling with dressing.