Preheat a saute pan over medium heat. Add 1 Tbsp olive oil to the pan. Cook the onion until translucent, 3 to 5 minutes. Add the mushrooms, asparagus, and a pinch of salt.
With the processor running, drizzle in just enough water so that the mixture becomes smooth, similar in texture to thick hummus (super-firm will require more water, normal extra-firm will need less).
Spoon the quiche mixture into the sauté pan with the vegetables, and stir to combine. Transfer the mixture to the prepared pie plate, and smooth the top with a silicone spatula.