Great idea. I like it a lot. I would suggest the following though. Most people are more concerned with what they can make with what they have.
Therefore, eliminate the need to pick a dish. Allow your user to select an ingredient, then narrow the list of options for further selections to only those ingredients that are common to dishes containing the selected ingredient.
For example, if you pick tomatoes, then parmesan, you can probably eliminate pickles from the list. Once they've selected the ingredients, then show them the list of dishes.
It'd be a nice touch to include if you have a limited quantity of something. Like... I have flour, salt, sugar, tomatoes, mozzarella cheese, but I only have two eggs; what could I make?
Therefore, eliminate the need to pick a dish. Allow your user to select an ingredient, then narrow the list of options for further selections to only those ingredients that are common to dishes containing the selected ingredient.
For example, if you pick tomatoes, then parmesan, you can probably eliminate pickles from the list. Once they've selected the ingredients, then show them the list of dishes.