Cut round steak into six equal-size portions. Place meat between waxed paper, or a zipper-lock bag, and lightly pound with a mallet (or heavy skillet) until about a 1/4-inch thick. Season meat with salt and pepper. In a medium bowl, combine bread cubes, beef broth, garlic and onion. Fry bacon in a large skillet until crisp. Remove cooked bacon from pan and drain on paper towels. Reserve 2 tablespoons of the bacon grease. Combine bacon with bread mixture.
Place pounded steaks on a flat surface and divide bread stuffing equally, about 1/3 cup each, onto meat. Roll each piece snugly and secure with a toothpick. Return skillet to burner and heat reserved bacon grease over medium-high heat. Place rolls in pan and brown evenly. Transfer rolls to a lightly greased baking dish.
To prepare gravy, melt butter in the same skillet over medium heat. Stir in flour and continue stirring until flour mixture (roux) is light brown in color, for about 3 to 4 minutes. Whisk in beef broth and water, a little at a time, to blend with flour mixture. Bring to a boil, reduce heat and simmer for 2 to 3 minutes. Stir in wine and mushrooms, and season to taste with salt and pepper.
Pour gravy over browned rolls, cover and bake in a preheated 350 degree oven for 50 minutes. Remove toothpicks before serving.
Editor's tip: For best results, trim the silverskin, gristle and bone from any antlered game steak before cooking.