Preheat oven to 350 degrees F.
Into a large, deep skillet, over medium heat, add vegan butter. When the butter is melted, add yellow squash and shallot. Cook for about 3 minutes, stirring frequently until softened. Remove from heat and set aside to cool.
Into a large mixing bowl, combine Cheddar cheese, Parmesan cheese, sour cream, sea salt, and ground black pepper.
To the cheese mixture, add the cooked yellow squash. Stir gently, turning over the squash slices until thoroughly coated.
Into a prepared 11 x 7-inch baking dish, spread the squash mixture.
Top with a layer of crushed butter crackers.
Bake 20 minutes.