"From the kitchen of Julia" or "From Julia's Kitchen" means that
Julia invented the recipe
or
Julia wrote down the recipe
or
Julia gave the recipe to the cookbook author.
If you get recipes from a lot of people and you want to remember (or write down) who gave you which recipe, you could use "From the kitchen of <person's name>." If you do not want to write or remember who gave you the recipe, or if you think Julia is lying when she says that she just created the oatmeal cookie recipe and you are pretty sure she read it in a different book, leave it out.