You get all the possible cooking recipes from the start: it just depends on what ingredients you have on hand. When you visit a cooking pot, you'll see all the available recipes, and when you have the right ingredients, the recipes will enable.
The stews and soup that you can make with cooking sell for a few gold and have some basic perks, but are not nearly as good as potions. In terms of what you can make with carrots and potatoes, there's:
carrots, garlic, raw beef, and salt pile
Increases max stamina by 25, stamina regeneration for 12 minutes
Cabbage potato stew
cabbage, leeks, potatoes, and salt pile
Restores 10 health and stamina
cabbage, leeks, potatoes, and tomatoes
Health and stamina regeneration for 12 minutes
leeks, potatoes, salt pile, and venison
Restores 15 stamina, health and stamina regeneration for 12 minutes
If you scroll over the other recipes while using a cooking pot, the items you need to make them are listed under the item detail box.