Pat the short ribs dry with paper towel. Generously season the short ribs with salt and pepper and set aside.
Heat the olive oil in a large braiser over medium heat until shimmering. Add the short ribs and brown on all sides. Transfer the ribs to a plate and set aside.
Add the shallots and garlic to the pan and saute until softened and lightly caramelized. About 5 minutes.
Deglaze the pan with the red wine and add the beef broth, vinegar, oregano, and red pepper flakes. Give the mixture a quick stir.
Add the short ribs back to the pot and bring the liquid up to a boil. Reduce the heat to a light simmer and cover.
Let the ribs braise for 2 hours or until the meat shreds easily.
Remove the ribs from the pot and shred the meat using two forks. Place the meat in a large bowl and set aside.
Quarter the potato and place it in a medium-sized pot. Add enough water to cover the potato. Place the pot over high heat and bring to a boil. Boil the potato until tender. About 15 minutes.
Drain the water and, using a potato masher, mash the potato. Add the potato to the short rib meat.
Stir the sour cream, chives, and salt into the rib/potato mixture until smooth.
Allow the mixture to cool completely.
For the Pierogi Skins
Sift flour and salt together in a large bowl. Using a wooden spoon, make a well in the center of the mixture.
Add the sour cream, egg, egg yolk, water and chives to the center of well. Lightly beat the wet ingredients using a fork.
Using a wooden spoon, start to push the dry ingredients into the wet until a shaggy dough forms.
Transfer the dough to a floured surface and knead it until firm and silky.
Wrap the dough in plastic wrap and place in the fridge until ready to use.
For the Chimichurri
Place all ingredients in a medium-sized bowl and whisk to combine.
Cover the bowl with plastic wrap and transfer the sauce to the fridge.
The sauce can be made up to 24 hours ahead of time.
To Assemble
Roll the dough out to a 1/4 of an inch thickness.
Using a 3-inch cookie cutter, cut out a series of rounds from the dough.
Place 1 tablespoon of the short rib filling on one side of the round. Fold the bare side over top of the filling and pinch the edges together to form a seal. Dust the pierogi with flour and set aside. Repeat until you run out of dough or filling or both.
When ready to cook, bring a large pot of water to a boil. Add the pierogies to the boiling water and cook for 3 minutes or until pierogies start to float to the surface.
While the pierogies are cooking, heat a tablespoon of oil in a large skillet until shimmering.
Transfer the cooked pierogies from the water to the hot skillet and fry until crispy and browned on both sides. About 2 minutes.
Transfer the pierogies to a medium-sized mixing bowl and add the chimichurri. Give the bowl a toss to coat the pierogies in sauce.
Divide the pierogies between six bowls and serve with a dollop of sour cream and sprinkling of pomegranate arils.