Whisk the flour and the salt together. Add the remaining ingredients and stir until a shaggy dough forms. Knead the dough until silky. Wrap the dough and chill for 1 hour.
Drain the potatoes and add the cheese, sour cream, butter, salt and a ton of pepper. Mash the potatoes until the butter melts and the mixture is smooth. Set aside to cool.
Place the shallots in a small saucepan and cover with the oil. Place the saucepan over medium-low heat. Cook the shallots, swirling occasionally, until golden.
Roll the dough out. Cut circles out of the dough using a biscuit cutter. Expand the circle a little. Add 2 tsp of the filling. Fold the dough taco-style. Pinch to seal the pierogi all the way around.
Once the water is boiling, salt the water and add your pierogis, working in batches. Cook the pierogis for five minutes.
Working in batches, fry the pierogis until golden. Top the radicchio with the golden pierogies and garnish with pecorino cheese, and fresh black pepper.