Yeah the cooking store during the cooking event that comes around every few weeks is the only place to get it unfortunately. Theres other ingredients that you can get only from there or from the mole mart if they happen to show up for you.
Cooking event or the Othenia, the endless steppe Golden Sea. You'll have chance to doing "cooking: find ingredients" and you'll have chance to get milk from there, also with salt/pepper/potato/flaxseed oil/leek/leaf pile