How to Make It
In a heatproof bowl, soak the morels in the boiling water until softened, about 20 minutes. Rub them to loosen any grit, then lift them out and coarsely chop.
In a large bowl, combine the flour with 1/2 teaspoon of salt. Add the eggs and stir until the dough just comes together. Transfer to a lightly floured work surface and knead briefly until soft and smooth. Wrap the dough in plastic and set aside at room temperature for 30 minutes.
Meanwhile, cook the potatoes in a large saucepan of boiling salted water until tender, about 20 minutes; drain. Return the potatoes to the pan and shake over high heat to dry them, about 1 minute. Using a potato masher, mash the potatoes. Mash in the milk, sour cream, Parmesan and butter. Stir in the morels and season with salt and pepper. Transfer to a bowl and let cool slightly.
Cut the dough in half and pat each piece into a disk. On a well-floured work surface, roll out the disks to 9-inch rounds. Cover with plastic wrap and let stand for 15 minutes.
On a floured work surface, roll out 1 round at a time to a 1/16-inch thickness. Using a 4-inch biscuit cutter, stamp out 9 smaller rounds. Lightly moisten the edge of 1 round and dollop 1 rounded tablespoon of the potato filling on half of it. Pat the filling slightly; fold the dough over the filling to form a half moon and press the edges to seal. Set aside on a floured platter. Repeat with the rest of the dough and filling.
Cook half the pierogies at a time in a large pot of boiling salted water until they rise to the surface, about 1 minute. Using a slotted spoon, transfer them to paper towels and dry. In a large bowl, toss the pierogies with just enough vegetable oil to coat.
Light a grill or heat a grill pan. Grill the pierogies over a hot fire, turning once, until browned, about 3 minutes per side. Remove from the grill. Add the celery leaves and grill until lightly charred, about 1 minute per side. Transfer the pierogies to a platter and garnish with the grilled celery leaves.
Make Ahead: The pierogies can be prepared through Step 5 and frozen for up to 1 month. Boil the frozen pierogies for the same amount of time indicated for the fresh ones.
Wine Recommendation: The rich, smoky filling in these pierogies makes them perfect foils for a full-flavored Merlot with velvety tannins like the 1994 Columbia Crest Estate Series from Washington State or the 1995 Meerlust from South Africa.