You can craft a savory tart with any number of crusts. Bubbly yeasted pizza dough, flaky pastry crust and crispy semolina flatbread to name a few; or you can make a crustless tart and make lots of folks happy. One of the current trends is to go paleo with crusts made from cauliflower, with or without cheese.
There was a vegan cheese spread I used a few years ago for a client who stopped eating dairy, with a persistent longing for the texture and taste of a creamy cheese, but with a strong dislike for the soy substitutes available. This cheese was made from oats and had a light caramel color and hickory smoke flavor. It was so delicious I purchased some just for me and indulged.