Split radicchio lengthwise and place in glass ovenware dish. Remove feet of portobellos. Split and place feet and caps in same dish. In a small bowl, mix vinegar, garlic, anchovies, marjoram and olive oil. Pour over radicchio and portobellos and let stand one hour.
In a 3 quart saucepan, heat water until boiling. Drizzle in polenta in a thin stream, whisking constantly, until all polenta is incorporated and mixture begins to thicken. Switch to a wooden spoon, pull off heat and continue to stir until thick as paste. Add stracchino, stir through and set off heat. Place portobellos and radicchio on grill and cook until just lightly charred on one side, about 4 to 5 minutes, and then turn. Cook 3 to 4 more minutes and remove, dredge in marinade and pace around perimeter of large platter. Pour polenta in center and serve.