Preheat the oven to 375 degrees F. Fit the eggless pie crust into a 9-inch pie pan, line it with parchment paper, and fill it with pie weights.
Bake the crust for 12 minutes. Remove the weights and parchment, then bake for another 5 minutes before setting the crust aside.
Heat the olive oil in a skillet over medium heat. Cook the diced onion for 4 minutes, then add the spinach and cook until wilted and excess moisture has evaporated.
Blend the tofu, whole milk, chickpea flour, cornstarch, nutritional yeast, Dijon mustard, garlic powder, turmeric, fine salt, and black pepper until completely smooth.
Stir the cooked onion, spinach, and 3/4 cup of the Gruyere into the blended filling. Spread the mixture evenly in the partially baked crust.
Scatter the remaining Gruyere over the top. Bake for 35 to 42 minutes, until the center is set and the top is lightly golden.
Cool the quiche for 20 minutes before serving. This resting time allows the creamy filling to firm without becoming dry.