Activate the yeast

• Whisk together the warm milk, sugar and yeast in a bowl until the yeast dissolves.
• If using active dry yeast, let it sit for about 5 minutes until foamy.

Make the dough

• Add the egg and egg yolk and mix well.
• Add the flour and salt and mix until a shaggy dough forms.
• Add the butter and knead until smooth and elastic and it passes the windowpane test.

Let the dough rise

• Place the dough in a lightly greased bowl and cover.
• Let it rise until doubled in size.

Cook the apple pie filling

• Melt the butter in a saucepan, then add the apples, brown sugar, cinnamon, nutmeg, salt and lemon juice.
• Cook over medium-low heat until the apples are tender.

Thicken the filling

• Mix the cornstarch with the water and add it to the apples.
• Stir until thickened, then remove from the heat and stir in the vanilla.
• Let cool completely, then transfer to a piping bag.

Shape and proof the bars

• Roll the dough into a large rectangle and cut into 10 equal bars.
• Place the bars on parchment paper, cover and let proof.

Fry the donuts

• Heat the oil to 180 °C.
• Fry the donuts until golden brown, turning once.
• Let cool slightly, then poke a hole in the center of each with a skewer or chopstick.

Make the maple glaze

• Mix the powdered sugar, maple syrup, melted butter and vanilla until smooth.
• Add milk or cream as needed to reach a dipping consistency.

Fill, glaze and finish

• Fill each donut with the apple pie filling.
• Dip each donut in the maple glaze and place on a wire rack.
• Let the glaze set before serving.