Jam & Bread Pudding

1 loaf brioche, sliced 1/2" thick
3/4 cup + 3 tbsp. strawberry preserves, divided use
4 large eggs
1/2 cup sugar 
2-1/2 cups + 1 tbsp. whole milk, divided use
1 tsp. vanilla extract
6 tbsp. unsalted butter or margarine, melted, divided use
3/4 cup confectioners' sugar
garnish: fresh strawberries

      Heat oven to 375ºF (190ºC).  Butter a 9x13" glass baking dish.  Arrange half of brioche along bottom of dish; cut or tear slices to fit.  Spread 3/4 cup jam on top; cover with remaining bread.  Whisk eggs, sugar, 2-1/2 cups milk, and vanilla; pour over bread.  Press to soak and brush top with 4 tbsp. melted butter.  Cover with foil and bake 15 minutes.  Remove foil, continue baking 15 minutes longer, or until pudding is set.  Remove from oven.  Heat broiler.  In a bowl, whisk remaining 1 milk with confectioners' sugar.  Stir in remaining butter and jam until mixture is smooth.  Spread mixture over top of pudding, place under broiler; broil until glaze is golden.  Serve hot or warm, garnished with fresh strawberries.