Preheat oven to 350 degrees. Lightly spray a 13x9 baking dish with cooking spray.
Place crackers into a gallon size resealable bag and crush with fingertips till they resemble small crumbs, set aside.
Bring a large pot of water to a boil. Add broccoli and cauliflower and boil for 3 minutes.
Drain into a colander, immediately rinse with cold water. Let drain for a minute or two and then place vegetables into a large bowl.
Melt 6 tablespoons of the butter in the same pot you cooked the broccoli and cauliflower in over medium heat.
Add the onions and cook until soft, about 3 minutes, stirring occasionally. Add the garlic and cooked one more minute.
Add the flour to the onions and garlic and whisk until smooth coooking for about 30 seconds.
Whisk in the milk and half-n-half and simmer till thickened, whisking constantly.
Remove from heat - stir in sour cream and add salt and pepper to taste.
Pour sauce into the bowl with the broccoli and cauliflower and mix together.
In a small bowl, combine the beaten egg, 1/2 cup of the shredded extra sharp cheddar cheese, 1/2 cup of the Italian blend cheese, and 1/2 cup of the crackers crumbs. Add cheese mixture to broccoli and cauliflower and combine well.
Transfer casserole to the prepared baking dish.
Melt the remaining 2 tablespoon of butter and pour into the bag of remaining cracker crumbs - mix well. Add in the remaining 1/2 cup of the shredded extra sharp cheddar cheese, 1/2 cup of the Italian blend cheese and mix into cracker crumbs. Sprinkle breadcrumb topping over the casserole.
Bake for 45 minutes, until filling is hot and bubbly. Check after about 30 minutes and cover with foil if topping is browning too quickly. Let stand a few minutes before serving.