Preheat the oven to 400°F. Line a baking sheet with parchment paper. Quarter the baby potatoes and add them to a large mixing bowl. Cut the cauliflower head into florets and add them to the same bowl. Set aside.
Open the can of chickpeas, rinse, drain, and pat dry. Add them to the baking sheet along with the quartered potatoes and cauliflower florets. Sprinkle the corn starch, olive oil, lemon juice, paprika, garlic powder, cumin, and salt over the vegetables. Stir to combine, then roast in the oven for 40 minutes, flipping halfway through, until the veggies are crispy.
While the veggies are roasting, make the tahini sauce. In a large mixing bowl, combine all the tahini herb dressing ingredients. Slowly add more water as needed until you reach a hummus-like consistency.
Add a large dollop of sauce to each serving bowl, then spread it with the back of a spoon so the bottom of the bowl is evenly coated. Once the veggies are done and have cooled slightly, pour the vegetable mixture over the sauce. Top with additional chopped parsley, everything seasoning, and more tahini herb sauce. Ready to serve!