Preheat oven to 375°. Line a large cookie sheet with parchment paper and spray paper with cooking oil spray, or brush with vegetable oil.
Lay one sheet phyllo on paper, and brush lightly with a little melted butter. Sprinkle with 1 portion of parmesan cheese. Repeat layering five more times.
Lay the last filo sheet on top, and brush with remaining butter and parmesan. Scatter onion across phyllo, top with mozzarella and arrange tomato slices in a single layer, overlapping slightly. Sprinkle with thyme, salt and pepper.
Bake until phyllo is golden, about 20-30 minutes.
Cool 10 minutes and then cut into squares and serve.