In a large bowl, whisk together flour, sugar, and salt.

In a separate bowl, dissolve yeast in warm milk. Let stand for 5 minutes.

Add melted butter and egg to the yeast mixture. Whisk to combine.

Pour wet ingredients into the dry ingredients and mix until a shaggy dough forms.

Knead the dough on a lightly floured surface for 5-7 minutes until smooth and elastic.

Place the dough in a greased bowl, turning to coat. Cover and let rise in a warm place for 1 hour, or until doubled in size.

In a saucepan, combine diced peaches, sugar, cornstarch, and cinnamon.

Cook over medium heat, stirring constantly, until the peaches soften and the mixture thickens (about 5-7 minutes).

Remove from heat and let cool completely.

Punch down the dough and roll it out to about 1/2-inch thickness.

Cut out donut shapes using a donut cutter or a round cookie cutter and a smaller cutter for the hole.

Place the donuts on a baking sheet lined with parchment paper. Let them rise for 30 minutes.

Heat vegetable oil in a deep fryer or large pot to 350°F (175°C).

Carefully fry the donuts for 1-2 minutes per side, until golden brown.

Remove donuts from oil and place on a wire rack to cool.

In a bowl, whisk together powdered sugar, milk, vanilla extract, and cinnamon until smooth.

Once the donuts are cool, dip the tops into the glaze.

Fill each donut with a spoonful of peach filling.

Let the glaze set before serving.