I believe you're looking for Extension:ArticleInclude. It allows you to overwrite the included article name with any random article on the wiki. It also allows you to limit the length, so that you only see a snippet of that article.
For your purposes, I'd imagine that the recipe title and/or ingredients would be sufficient. Including the ingredients may be tricky, since you list them at the top of the page in a simple list format. If you choose to go with the ArticleInclude extension, I'd recommend keeping your ingredients on a single line, and creating line breaks with HTML so that you could use the lines option to get what you need reliably.
Example, altered from Torta aromática:
<blockquote> 3 huevos <br> 3 cucharadas de leche <br> 6 cucharadas de manteca derretida <br> 1 ½ tazas de harina <br> ¾ tazas de azúcar <br> 2 cucharaditas de polvo de hornear <br> 2 cucharaditas de canela <br> ¼ cucharadita de clavo de olor molido <br> ½ cucharadita de cáscara de limón rallada </blockquote>
Relevant Options:
random: Overides article and shows a random article of the given namespaces
count: How many letters will be shown, negative values will display the whole article removing the specific number of letters from the end
lines: Count lines (not letters) that will be shown
Edit: If you don't want to bother with an Extension, Transclusion comes out-of-the-box since MediaWiki 1.8, but not with a random article function. You may have seen transclusion in action before on new user talk pages, where many wikis will commonly link to a page with helpful suggestions for new users.