Heat oven to 350 degrees F. Grease 12 regular-sized muffin cups with butter or cooking spray.
In a medium bowl, whisk together Bisquick mix, Italian seasoning, 1/4 cup milk, butter and 1 egg until soft dough forms. Divide into 12 equal pieces, and press into each muffin cup to cover the bottom and sides. Bake 8-10 minutes or until golden brown.
Meanwhile, in a large bowl, whisk together the 5 remaining eggs, remaining 1/4 cup milk, salt and pepper; set aside.
In a 10-inch nonstick skillet, heat olive oil over medium heat. Add zucchini, squash, tomatoes and onion and saute for 3-5 minutes, stirring occasionally, until the onions are cooked. Add the egg mixture to the vegetables, and cook for an additional 1-2 minutes, stirring occasionally, until eggs are loosely set. Gently fold in cheese.
Remove biscuit cups from oven. Using the back of a spoon, press the puffed crust into the cup to make a deep indentation. Spoon egg mixture into cups. Then bake for 10-15 minutes or until eggs are just set. To remove from pan, run a thin knife around the biscuit cup and lift out. Garnish with fresh basil.