I got some Monster Extract from a quest, and also can buy some from the Monster Shop.
What does it do? Does it extend the effect in the food like salt, or does it do something else entirely?
Monster Extract's main uses are:
Randomly restores or removes Heart Containers
Cooking Ingredient
In terms of being used for cooking, it looks like it has a very high chance of greatly increasing your meal's potency. From this PSA:
I found and tested a way to make maximum potency, 30-minute dishes using Monster Extract. This relies on you being pretty late in the game (consistent access to Monster Extract consistent access to the recipe parts you need), but it's pretty simple!
Basically, to make a 30-minute food item, your recipe should be:
2 Fruits with your intended status
2 Mushrooms with your intended status
Monster Extract
I have not yet found a stealth fruit, but this works with all resists (fire/ice/elec), haste, power up, and defense up (pumpkins are fruits for these intents and purposes).
Feel free to let me know if a recipe you use doesn't work - but I've yet to have it fail!
UPDATE: Because Monster Extract is random (and I'm apparently lucky as hell), this is not guaranteed, but this seems to have a VERY HIGH chance. Just throw a few of this recipe at it and hope for the best.
Monster Extract is a "filler" ingredient that can be used in both food recipes and elixirs. It randomizes up to three things (if applicable to the recipe):
Cooking with monster extract will never result in a "critical" success (with an additional bonus), even if cooked during a blood moon.
This answer is based on both my own experimentation as well as the following sources:
I have also noticed if you have the DLC it also doubles amount of fuel for the master cycle
ex. use 4 ancient screws + 1 monster extract = the equivalent of 8 ancient screws