Pat veal shanks dry with paper towels, then season with the salt & freshly ground pepper.
Add flour to a shallow dish. Add each shank to the flour, one at a time and turn to coat. Brush off excess flour.
Select brown/sauté (high heat) setting on a 6-quart electric pressure cooker. Add ½ teaspoon oil (for each shank that will fit without overcrowding), then brown the shanks for about 4 minutes per side. (1-2 shanks at a time). Remove shanks from the pressure cooker to a platter or plate and set aside.
Melt butter, then add the onions, celery and carrots and sauté for 4-5 minutes, stirring occasionally.
Add the garlic and tomato paste and cook for 1-2 minutes.
Pour in the wine and boil for 2 minutes, scraping the bottom of the pan to loosen any browned bits.
Add in 1 ½ cups mushroom/chicken broth, tomatoes, mushrooms, spices, bay leaves, then nestle the veal shanks into the liquid (add up to additional ¾ cup of broth if needed to just cover the shanks).
Lock lid; close pressure-release valve. Set to pressure-cook on HIGH for 45 minutes.
While the veal cooks make the Saffron Rice and Gremolata (instructions below).
Once the time has elapsed on the veal shanks, let the pressure naturally release for 10 minutes, then quick release any remaining pressure.
Remove meat and vegetables from the pressure cooker to a clean platter, discard bay leaves,remove meat, strain sauce, reserving strained sauce and mushrooms only. Cover shanks & mushrooms with foil and keep warm.
Skim fat from remaining juices. Select brown/sauté setting and adjust for high heat. Bring to a boil.
In a small bowl, mix cornstarch and water until smooth; stir into cooking juices. Return to a boil, cook, and stir occasionally until thickened into a silky gravy. 6 to 10 minutes.
Turn off the pressure cooker.
To serve, place hot rice on a platter, arrange shanks and mushrooms on the rice. Pour over a little gravy, then finish with a sprinkling of pomegranate seeds and gremolata.
Serve with remaining gravy, pomegranate seeds, gremolata, and your favourite vegetables.