Preheat oven to 350°F, and prepare a Bundt pan with nonstick cooking spray.
Cut each of the refrigerated biscuits into quarters, and flatten each piece using the palm of your hand.
Apply a thin layer of Dijon mustard to the center of the dough.
Place a piece of ham, a piece of turkey and about a teaspoon of Gruyere on top of mustard layer.
Fold up the sides of the dough until the meat and cheese are completely enclosed inside the dough.
Repeat with all dough pieces.
In a small bowl, whisk together the eggs and milk.
Place the turbinado sugar in a separate bowl.
Working one at a time, dip each ball into the egg mixture, shaking off the excess, followed by a dip into the sugar.
Place each ball into the prepared Bundt pan as you go.
Repeat with all stuffed dough balls.
Once the Bundt pan is full, drizzle the melted butter evenly over the top.
Bake for one hour, until golden brown and just firm to the touch.
Remove the monkey bread from the pan by turning the Bundt upside down, and carefully flipping it onto a cake stand or large plate.
In a small bowl, whisk the raspberry jam, adding a tablespoon of warm water if needed.
Lightly dust the powdered sugar over the monkey bread using a sifter, and drizzle with raspberry jam.