In a large bowl, combine the all-purpose flour, rye flour, sugar, and salt.
Add the cold, cubed butter to the dry ingredients. Use a pastry cutter or your fingers to mix until the mixture resembles coarse crumbs.
Beat the egg and add it to the mixture. Mix until combined. Gradually add cold water, one tablespoon at a time, until the dough comes together.
Form the dough into a disc, wrap it in plastic wrap, and refrigerate for at least 30 minutes.
In a large bowl, combine the grated carrots and potatoes. Mix in sugar, ground caraway seeds (if using), and ground cinnamon.
Stir in the milk and egg until well combined.
Preheat your oven to 375°F (190°C). Grease a muffin tin or line with paper liners.
On a floured surface, roll out the chilled dough to about 1/8-inch thickness. Cut into circles that are slightly larger than the cups of your muffin tin.
Gently press the dough circles into the muffin tin, making sure they cover the sides and bottom of each cup.
Spoon the carrot and potato filling into each pastry shell, smoothing it out.
Bake in the preheated oven for 25-30 minutes, or until the edges of the pastry are golden brown and the filling is set.
Allow the Sklandrausis to cool in the tin for a few minutes before transferring to a wire rack to cool completely.
Enjoy your meal!