It seems we all jumped to "Potluck" - which is great - but how about having your guest bring something w/o them knowing it's a potluck??? (tell them of course -as not to decieve them)
How about a cook-off or "Iron Chef"
A chili cook off? spaghetti sauce (you can provide the noodles) Hamburgers
Get creative with your "evites"
...You are invited to celebrate _____1st Birthday. This years celebration will be a competition...which of you is the best______ (filling in the blank) cook. Bring your ____ ready to serve.
Winner gets to a special treat (maybe slicing the cake with the baby?)
If you do spaghetti or chili - you can provide noodles or baked potatoe, rice
If you do burgers, you can provide buns and condiments
ALSO - you can have different competitions - main course, best salad or side dish, dessert and speciality drink
Just be sure the "winners" get a prize - like I said, cutting the cake or group winners photo with the baby, I'm sure you can figure it out
Themed "cook -offs" work well too - mexican or italian
I was kind of wordly huh?
Good luck