For sauce: Whisk all ingredients in a bowl, adding water as needed to achieve desired consistency.
Preheat oven to 400 degrees. Arrange vegetables on large baking sheet, (try to keep them from touching each other so they get crispier) and drizzle with olive oil, salt.
Stir to distribute, then put into oven for 20 minutes, until crispy and browned. Remove from oven, arrange on a plate, and drizzle with the tahini sauce and a little extra chopped parsley.