How can I spice up ground beef without using pepper? I cooked up some good-quality minced beef yesterday with salt, onion, and breadcrumbs. (I wrapped it around hardboiled eggs and baked it.)  I didn't use any pepper because I have allergies, and I didn't like the way it came out - it was bland and had a faint meaty "off" taste even though I knew it was fresh enough.  

I don't insist on it being hot and spicy, but what could I use to give it flavour? What is a good replacement that will flavor meat the way pepper would? Or at the very least, what spice or combination of spices would cover up the faint off taste? I know that medieval cooks used to use spices to cover "off" flavours in meat, but I think they were ones we use in sweet dishes now.

Tomato is not an option for me sadly but onion and garlic are fine.

I hope you can help, I'm finding this really intriguing.  I'm learning a lot about what pepper does just by going without.
Ground allspice berries and rosemary can add that piquant taste that you may otherwise be missing from the pepper.