Place sliced baguettes in a large bowl or pot. Cover with cream and milk. Let soak 1 hour or overnight. Mix only enough to let the pieces on the top get turned under and soak for another 15 minutes.

Preheat oven to 350°. Mix by hand the remaining ingredients until homogenous. Combine the bread with the remaining ingredients taking care not to over mix or destroy the integrity of all bread slices.

Grease a 2” deep 9” x 13” pan well and pour in the pudding. Cover with an inverted 9” x 13” pan, to leave space for the pudding to rise. Bake until set, about 1-1/2 hours. The pudding should have at least 1/2 inch of rise. Once set, remove cover and brown the top for about 15 minutes. Remove from oven, cut into 12 pieces, 4” x 3”, and cover with rum sauce.

Mix all ingredients until homogenous. (The sauce can be made ahead of time and re-stirred.) Slowly pour sauce over hot bread pudding, taking time to get sauce all around the edges and in each corner by lifting individual pieces away from the sides and bottom of the pan. Best served hot.