Preheat an oven to 350℉.
In a large bowl, mix the pesto, spent almonds, spinach, and hummus. Set aside.
Use a half sheet pan (18” x 13”), or a large cookie sheet, and lightly brush with melted vegan butter using a pastry brush. Roll out the phyllo dough on a clean surface, and cover with well wrung out paper towels to keep the dough from drying out (it will dry out fast, and will crumble like dry paper if you let it sit for too long).
After brushing the cookie sheet, carefully place one sheet of phyllo on the cookie sheet, and brush with butter. Continue layering until you’ve got 6 sheets of phyllo, brushing the top of each one lightly with butter.
Once you’ve got 6 sheets, carefully spread the filling over the entire sheet, leaving 1 inch border. Cover with a phyllo sheet, brush with butter, and continue layering for an additional 5 phyllo sheets (for a total of 6 on top), finishing with a generous brushing of butter. Fold the edges under to create an outer crust, and then carefully cut into 12 squares. Using a sharp knife, make two cuts long-ways, and three cuts short-ways.
Sprinkle with sesame seeds, and bake in the oven for 60 minutes, or until the pastry is golden brown. Serve with your favorite sauce, and enjoy the flaky goodness!