Make the filling: Beat the softened cream cheese with a hand mixer or a sturdy fork in a medium bowl until smooth. Add the pumpkin puree, powdered sugar, 1/2 teaspoon of the pumpkin pie spice, and 1/2 teaspoon vanilla. Mix until fully combined and creamy with no streaks. Set aside.

Make the custard: Crack the eggs into a shallow bowl wide enough to fit your bread. Add the milk, granulated sugar, the remaining 1/2 teaspoon pumpkin pie spice, and 1/2 teaspoon vanilla. Whisk until the eggs and milk are fully blended with no streaky egg whites visible.

Assemble the stuffed slices: Spread a generous layer of the cream cheese filling on one side of 4 bread slices, going nearly to the edges. Top each with a second slice of bread and press gently all around the edges so the filling is sealed inside. Do not press so hard that you flatten the bread.

Dip the sandwiches: Carefully lower one stuffed sandwich into the custard. Let it soak for about 20 seconds per side, tilting the bowl slightly to help the custard reach the edges. The bread should be coated but not falling apart. Repeat with the remaining sandwiches.

Cook: Melt 1 tablespoon of butter on a griddle or large skillet over medium heat. When the butter foams and the foam starts to subside, add 2 stuffed sandwiches. Cook for 3 to 4 minutes on the first side until the bottom is a deep golden brown. Flip gently with a wide spatula and cook another 3 to 4 minutes. Add the remaining butter and cook the second batch the same way.

Serve immediately with a drizzle of maple syrup and a light shake of cinnamon over the top. Slice each piece on the diagonal if you like to show off the cream cheese filling inside.