Preheat your oven to 375°F (190°C). Grease a muffin tin and line with parchment paper for easy removal.
In a mixing bowl, sift together the flour, granulated sugar, salt, and baking powder.
In another bowl, whisk together the melted butter, milk, and vanilla extract until well combined.
Gradually pour the wet ingredients into the dry ingredients, mixing until just combined.
In a small bowl, combine the diced peaches with cinnamon, nutmeg, and brown sugar to create the filling.
On a floured surface, roll out the dough into a rectangle about ¼ inch thick.
Cut the dough into long strips and layer them on top of each other, slightly overlapping. Roll the strips into a log shape, then slice the log into 12 equal pieces.
Take each piece and place it into the muffin tin cavity, pressing down gently while making sure to leave some of the dough overlapping the edges.
Spoon the peach filling into each cruffin base.
Fold the dough over the filling slightly, if needed, and brush with the beaten egg to give it a golden finish.
Bake in the preheated oven for 20-25 minutes or until golden brown and cooked through.
Allow the cruffins to cool in the tin for about 5 minutes, then transfer them to a wire rack to cool completely.