Grease a 9x13 inch baking dish.
Cut bread into 1 inch squares and spread in the prepared baking dish. Ideally, leave this bread out for a few hours to become a bit stale. This will help your casserole to not get too soggy. Alternatively, stale the bread using your oven. I turn my oven up to 350 and then turn it off, leaving the bread in for about 30 minutes.
Combine blueberries, 2/3 cup sugar, vanilla, 1 Tbsp lemon juice, water, and a sprig of rosemary in a heavy saucepan. Bring to a boil on high heat, stirring occasionally. Once it hits a boil, reduce it down to medium-low heat and simmer until thickened, about 20 minutes. Allow to cool. Remove rosemary.
Completely combine goat cheese, 1/2 tsp vanilla, powdered sugar, and lemon zest. Mixture should still be crumbly.
Whisk eggs, milk, cream, 1/4 cup white sugar, 1/4 cup brown sugar, cinnamon, and 1 1/2 tsp vanilla and whisk to combine.
Evenly drop one tablespoon of your blueberry sauce and 1 teaspoon of your blended goat cheese mixture onto the bread.
Pour your custard mixture over the entire dish, covering completely. Press down with your spatula slightly to assure full coverage.
Cover and refrigerate for at least 3 hours or overnight.
Preheat oven to 350.
Stir to combine Bisquick, sugar and butter. It should be crumbly.
Remove the goat cheese and blueberry French toast casserole from the refrigerator and sprinkle the crumb topping evenly on top.
Bake for 45-50 minutes. Allow to cool for 5-10 minutes before serving.