For brioche: place all ingredients except the butter in a mixer equipped with a dough hook (preferably a kitchen aid k5). Mix on slow speed for 7 minutes until the dough has come together and is elastic and smooth Increase the speed of the mixer to medium and gradually add the butter in small pieces waiting for each piece to be absorbed in the dough before adding the next. This process will take at least 7 more minutes until all the butter is incorporated in the dough. When finished the dough will be very smooth, elastic, velvety and extremely soft. It is important not to add more flour to the dough, it should be extremely soft. Place dough in refrigerator overnight or for at least 6 hours. After dough has rested divide in 2 pieces and shape into logs of 8 inches long and 3 inches across. Place in a warm draft free place approximately 80 degrees and cover with a damp cloth It will take at least 2 hours for the bread to double in volume, eggwash with a mixture of whole eggs and heavy cream and bake in a 375-degree oven for 50 minutes until golden brown and hollow sounding. The bread should completely cool before slicing. It would probably be best if brioche be made the night before the French toast is to be made.
For the French toast: Blend all ingredients together, place in a low flat-bottomed baking dish large enough to accommodate the whole slices of brioche. Slice brioche to 1 inch thick slices, soak in egg mixture, be sure the slices are saturated. Heat a large cast-iron skillet to medium heat, add 1 tablespoon of butter and cook Fench toast for about 3 minutes on either side until golden brown. Serve immediately with warm maple syrup.