This is largely affected by your contribution points and current cooking level (Beginner - Guru), so please adjust the recipes accordingly.
Once you've established your cooking level, visit the nearest Imperial Crafting Delivery NPC by clicking the magnifying glass icon beside your minimap, type Imperial Crafting. This will show you the different NPCs, choose 1 closest to you.
Interact with the NPC, here I chose Bech in Calpheon City, and click the "Imperial Craft..." and by default this will be on Food, the other option being Medicine (Imperial Alchemy).
2 panels will pop-up. On the left you can see your Daily Delivery Quantity, which is affected by your Contributions Points, this is higher if you have more CP. And the available Cooking Boxes for exchange per level. If either of these 2 values in 0, you cannot exchange any boxes. Daily Del Quantity resets after 00:00, available cooking boxes reset more often within the day, but I personally have only tried it after the 00:00 reset.
On the right side, you will see the panel indicating how much Imperial Cooking Boxes you have.
To help you decide which recipe to make to turn into Imperial Cooking Boxes, you can hover your mouse on top of the multiple chest icons beside their available number of exchanges. Now all you need to do is prepare the food required for the box, then process it in L via Imperial Cuisine to turn them into the required box.
NOTE: I turn all of the output from cooking into boxes, including the higher level ones that were made. I stack them in storage, and just exchange the maximum number based on my Daily Delivery Quantity.
Below I open Imperial 500 [Cooking] Special Delivery Gift Boxes. You get these before for every box exchange. Sadly this has been discontinued.
- Beginner 1