Cheesy Broccoli Vegan Quiche [Gluten-Free]

gluten-free, vegan frozen pie crust, unthawed ((I used Wholly Wholesome brand))

olive oil

heaping cups broccoli florets, fresh or frozen and brought to room temperature, chopped into smaller pieces if desired ((*If using frozen, see note below))

chopped onion

Kosher salt

silken tofu, excess water drained

plain, unsweetened soy milk

nutritional yeast

mustard powder

ground nutmeg

freshly ground black pepper

vegan cheddar-style shreds