Fill a large pot with water; bring to a boil. Add potatoes; cook for 10-15 minutes, until potatoes are fork tender. Drain; return potatoes to pot. Add nutritional yeast, oil or butter, salt, pepper and turmeric.
In a medium skillet over medium heat, warm 1 tablespoon oil. Add mushrooms; cook for 10 minutes, stirring often, until mushrooms are lightly browned. Add garlic; cook for 1 minute, until fragrant. Add flour and starch; stir to coat mushrooms evenly and remove any chunks. Slowly pour in broth, stirring constantly. Reduce heat to simmer and cook until gravy is thick but pourable. Add thyme, salt and pepper; stir. Remove from heat.
Serve a scoop of mashed potatoes with a veggie burger topped with mushroom gravy. Add sauteed greens, if desired.