buy a mayonaise maker from saibara or cook one. here is the recipie:
Mayonnaise (S): Whisk, Vinegar ; Regular Egg, Oil
Mayonnaise (M): Whisk, Vinegar; Good Egg, Oil (Won: 157G)
Mayonnaise (L): Whisk, Vinegar; High Quality Egg, Oil
Mayonnaise (G): Whisk, Vinegar; Gold Egg, Oil
Mayonnaise (P): Whisk, Vinegar; P Egg, Oil
Mayonnaise (X): Whisk, Vinegar; X Egg, Oil
Mayonnaise (X) (alternative recipe): Mayonnaise (S), Mayonnaise (M),
Mayonnaise (L), Mayonnaise (G), Mayonnaise (P)
N.B. Mayonnaise (X) can be made in your Mayonnaise Maker using an Egg

once you upgrade your chicken coop you can buy a mayonaise maker

Easy! all you got to do is follow these steps:
1. Get your chicken coop upgraded
2. Buy a mayonaise maker
3. put a egg in

And VOLA! Mayonaise! ( the size of the mayonaise depends on the egg)