Cook rice according to directions; set aside. This can be done the night before.
Preheat oven 350 degrees.
Grease 11x14" baking pan.
With sharp knife cut core from cabbage. Wrap in clean dishtowel and microwave approximately 10 minutes. Begin by pulling off the outer leaves as they just become limp and pliable; set those aside. Replace remaining dishtowel wrapped cabbage in microwave for 5 minutes, repeating the process of removing limp leaves until all leaves have been removed and are relatively soft.
In the meantime, should you need to grind your ham seasoning, place in food processor and pulse until the ham resembles ground beef. It will be a looser consistency.
In large, heavy bottomed pot or Dutch oven, fry ground beef and ham together until beef turns brown, breaking up chunks. Allow about 1/4 cup or so of the liquid to remain in the bottom of the pot.
To the ground beef/ham add onions, bell pepper, garlic and cook until vegetables are limp, about 4-5 minutes. Add the parlsey and mix.
Add paprika and season with salt and pepper to taste.
Add 1/2 cup breadcrumbs and mix well, allowing it to absorb any liquids.
Add cooked rice and toss until thoroughly incorporated. The mixture should appear relatively dry; if not, add additional breadcrumbs.
Cup each cabbage leaf individually and spoon meat mixture into the center and fold over sides. Place side-by-side each cabbage bundle into prepared pan. Repeat this process until all cabbage leaves are filled.
In a small bowl, combine tomoto sauce and sugar; mixing well.
Spoon a small amount on top of each cabbage bundle; spreading as you go.
Mix beef bouillon cube with 1/3 cup water and pour into corner of pan, avoiding pouring over cabbage and tilting pan to distribute.
Wrap pan tightly with aluminum foil and bake in preheated oven for 45 minutes. Open carefully.
Note: Should you have more rolls than can fit in the pan, prepare additional pan. Should you have more filling than cabbage leaves, place mixture in a greased oven-proof casserole or ramekin. Top with butter and parmesan cheese and bake for about 20 minutes.