Line a large baking sheet or counter surface with parchment. Lightly flour a large work surface.
Divide the rested dough into 2 equal pieces. Place one piece on work surface and place the other back in the plastic wrap.
Roll the dough into a thin sheet, dusting with flour as needed to prevent sticking, until it is about 1/8 inch (3 millimeters) thick.
Use a 3 inch (7.5 centimeter) wide circular cutter or the top of a glass to cut out circles of dough. Gather up the scraps and add it to the covered piece of dough.
Place two or three strawberry pieces in the center of a circle.
Fold the circle in half over the strawberries to make a half moon shape, lightly pressing around the filling to remove any air pockets as you press down to seal the edges. If desired, use a fork to crimp around the edges. Place on prepared parchment in a single layer and repeat with remaining dough and filling.
Bring a large pot of salted water to a boil. Add a few of the pierogi, taking care not to overcrowd, and stir gently to separate from the bottom.
Cook until the Pierogi float to the top, then a couple minutes more to make sure the strawberries are tender, about 5 minutes total. Use a slotted spoon to remove, drain, and repeat with remaining Pierogi.
In a small bowl, stir together the sour cream and sugar, adjusting sugar to taste.
Serve the boiled pierogi immediately with dollops of the sour cream, additional strawberry quarters, and fresh mint leaves for garnish.