Preheat oven to 425°. Roughly chop marjoram leaves (if larger than a ladybug) and reserve a heaping tablespoon.
Remove crusts from bread, then break bread into bite- size pieces. Measure 3 cups (loosely packed) and put into a bowl. Pour milk over bread and stir so all of it gets soaked. Crack eggs into a second bowl and remove any shell with a small spoon.
In a large bowl, combine beef, 1/2 tsp. salt, and about 1/4 tsp. pepper. Grate garlic into meat, using smallest holes of a box grater. Mix in egg, cheese, mustard, and marjoram with your just-washed hands.
When bread is soft, break it up by hand into very small (roly-poly–size) shreds. Mix soaked bread into meat.
Form mini meatballs by rolling about 2 tsp. meat between the palms of your hands. Arrange on 2 baking sheets in one uncrowded layer
Bake until well browned and cooked through, 15 to 18 minutes (cut one open to check). Scoop into a serving bowl and turn off the oven.
To make sandwiches, spoon some tomato sauce onto a roll and top with 5 or 6 meatballs. Add a little more sauce and sprinkle with grated Parmesan cheese.
MAKE AHEAD Cooked, cooled meatballs, up to 1 day, chilled, and up to 3 months, frozen. Thaw and reheat, uncovered, at 350° for 15 minutes.