Place first five ingredients in Instant Pot insert. Place rinsed corned beef on top, sprinkle with contents of seasoning packet and bay leaf. Cover with 4-6 cups water to cover (I used 5 cups water). Seal pressure cooker and cook at high pressure for 85 minutes. When finished, let pressure naturally release for 20 minutes.
Open Instant Pot and remove corned beef to shallow dish. Strain cooking liquid and return to pot. Cover corned beef with 1½ cups cooking liquid to keep from drying out, loosely cover with foil.
In 3-4 cups of remaining cooking liquid in the insert, add the chopped parsley, a generous pinch of salt and some cracked pepper, then the potatoes, carrots, parsnips and red onion. Top with the cabbage wedges. Seal and cook on high pressure for 3 minutes. Quick release the pressure.
To serve, slice corned beef and arrange in center of large platter. Surround with vegetables, preferably grouped together by type, it's more pleasing to the eye and easier for guests to choose what they want. Ladle some cooking broth over meat and vegetables. Sprinkle with some chopped parsley and serve with horseradish cream sauce on the side.
To make horseradish cream sauce: Whip heavy cream until soft peaks form. In a separate bowl, combine mayo, horseradish and mustard. With a spatula, fold in the whipped cream until combined. Add a pinch of sugar and salt and pepper to taste. Transfer to serving bowl and refrigerate until ready to serve.