Grate sweet potatoes and squeeze until dry. In a large bowl, mix sweet potatoes with 2 TBs oil, salt and pepper. Oil a pie dish, and arrange sweet potatoes in the shape of a pie crust.
Arrange whole peppers and cherry potatoes on a baking sheet. Drizzle with oil and roast on high heat (450F) until the skin on the sweet potatoes begins to scorch in places, approximately 25 mins.
While crust is baking, coat a baking sheet with aluminum foil. Arrange tomatoes and whole bell peppers, drizzle with 2 tablespoon olive oil and a healthy pinch each salt and pepper and toss to coat. Place in the 450 degree oven with the crust. Continue baking after crust is done, turning bell peppers over to ensure all sides darken evenly. The crust is ready when the tomatoes have burst in parts and the bell peppers have blackened fairly evenly - about 30 minutes in total. Place bell peppers into a ziploc bag, seal and allow to sweat for about 10-15 minutes. Peel peppers and cut them into strips. (these two stages can be done in advance).
To prepare quiche filling, add drained tofu to a food processor with nutritional yeast, hummus, garlic cloves, cumin, sea salt and pepper and optional red pepper flakes. Process until smooth.
Add roasted peppers and tomatoes to a mixing bowl and top with the tofu mixture. Toss to coat. Fill quiche crust with mixture, spreading it into an even layer and smoothing the top.
Bake quiche at 375 degrees for a total of 30–40 minutes, until top appears golden brown and firm. If the crust browns too quickly, loosely cover the edges with foil.
Let cool briefly before serving. To reheat, place in a 350F-degree oven for 5-10 minutes, taking care not to burn the edges.