Preheat the oven to 375°F. Line a baking sheet with parchment paper or use a nonstick baking sheet. Lightly roll out the puff pastry, then cut the pastry into shapes that reflect the shape and size of the dishes or bowls you wish to serve the stew in (I made little hearts this particular day). Beat the egg with a splash of water and arrange the cut pastry on the baking sheet. Brush the dough with the egg wash and bake to golden, 20 to 25 minutes.
While the pastry is baking, in a large pot, melt the butter over medium heat. Add the ramp whites, onions, garlic, celery, carrots, and potatoes; season with salt and pepper. Partially cover and let that cook until the vegetables are tender.
Sprinkle with the flour and stir to combine. Add the poaching liquid and cook, stirring well (really work the bottom of the pot to make sure you don’t get any roux sticking on the bottom), until thickened.
Add the cream if you want; I added the cream because the baby [Viv] really loves cream of chicken soup, but it isn’t really necessary—it’s gilding the lily. Add the mustard, peas, ramp greens, asparagus, tarragon, and parsley. Add the chicken and as soon as the peas heat through and the asparagus is tender-crisp, you’re ready to serve it up.
Ladle the chicken mixture into bowls and put the puff pastry up on top (the baby loved it).