You have to pick a primary relationship direction. Base your decision on which way you’ll most frequently create/edit the relationships. E.g. if you want to make recipes and then add eggs to them, have a Lookup column in the recipes table.
In the ingredients table, make a lookup column. When choosing lookup column, there’s an option for “Referenced By” - choose this to see all recipes that reference this ingredient.
I’d suggest using an approach to many-to-many relationships that comes from the relational database design world. Many-to-many relationships involve three tables. In your example, they would be: Recipe, Ingredient, and an “association” table. This association table features lookups to the Recipe and Ingredient tables. To help make it clearer, I created a barebones example of the three tables on this doc: Many-to-Many. You can create views, filters, and sorts on the association table that satisfy your information needs.