Heat oven to 400°.
Line a baking sheet with parchment. To make the spiced squash hummus: Using an immersion blender, whisk the chipotle paste and 1 tablespoon extra-virgin olive oil into the squash mash until it is smooth (at this point you could serve it as hummus with toasted pita bread).
Spread squash hummus on the flatbreads. Cook the sliced shiitakes in a nonstick pan until soft, sprinkle with a little salt and divide over the flatbreads. Crumble feta across the flatbreads. Bake for 10 minutes in the oven.
Take the flatbreads out of the oven and garnish: drizzle some extra-virgin olive oil, lemon zest, pumpkin kernels and sumac.