Preheat the oven to 375 degrees Fahrenheit.
Add all of the seasonings to a small dish and set aside.
Add chopped sweet potatoes and 1 ½ tablespoons olive oil to a large mixing bowl. Add ½ of the seasoning and toss to coat. Add to sheet pan and bake for 10 minutes.
Add zucchini, red pepper, and corn to the same mixing bowl and toss with the rest of the olive oil and the seasoning. Add to the sheet pan with the potatoes and bake until everything is fork tender, about 25-30 minutes.
Remove sheet pan from the oven and stir in black beans and sprinkle with cheese (if using). Bake for another 5 minutes or until cheese is melted and beans are warm.
While the sheet pan is in the oven, puree the sauce ingredients together in a food processor until smooth. Add more water if you prefer a thinner sauce.
