In a small bowl, stir together the cornstarch and 2 tablespoons of the juice from the tomatoes; set aside.
In a large saucepan, cook and stir the onion and garlic in the 1 tablespoon of butter until tender. Carefully stir in the undrained tomatoes, the okra, sugar, basil, hot pepper sauce, and salt and pepper.
Stir the cornstarch mixture, then add it to the vegetable mixture. Cook and stur until the mixture is thickened and bubbly. Remove from heat.
Pour the vegetable mixture into a 2-quart rectangular baking dish. Dot with the 2 tablespoons butter. Cover and bake in the oven for 20 minutes.
Remove the casserole from the oven. Sprinkle with the stuffing mix and the cheese. Return to the oven; bake about 5 minutes more or until stuffing mix and cheese are golden brown.