In a stand up mixer, cream together vegan butter and sugar. With mixer on, add pumpkin, apple sauce, and vanilla, scraping down the sides of bowl as needed. The batter will curdle at this point; don't worry, it will come back together.
In a small bowl mix together flour, baking powder and soda, and spice. With mixer on low speed, add flour mixture to butter/sugar mixture in 3 batches, stopping to scrap down the sides of the mixture in between. Blend until just combined.
Pour the batter into the prepared 8x8 baking pan, top with streusel, pressing down lightly, and bake for 45-50 minutes or until a knife inserted in the middle comes out clean.
Remove from oven and let cool for 20 minutes before cutting and serving.