In a medium sauce pan, over medium heat, add butter and brown sugar and cook until butter and sugar have melted, about 1-2 minutes. Add apples and sprinkle with cinnamon. Sauté until apples have softened and caramelized, 4-5 mins turning carefully. Set aside.
To make caramel sauce: Spread sugar evenly into the bottom of a heavy duty stainless steel sauce pan, Pour in water, and heat over medium heat without stirring.
Bring to a boil. The sugar will begin to bubble and dissolve. If any undissolved sugar remains, gently swirl the pan to help it dissolve.
Watch for the color to change from clear to golden amber, the caramel should begin to slightly smoke then deepen to a reddish-brown color.
Once it reaches the reddish-brown color, immediately remove from heat, and stir in remaining ingredients. Stir with a clean heat-proof spatula or wooden spoon until smooth.
Bring a large pot of water to a boil. Boil perogies and stir occasionally for 6 mins. Drain and divided into 4 dessert bowls. Top each with apples and drizzle with caramel sauce.
Once remaining caramel has cooled, you can pour into a glass container, cover and refrigerate.