Cook the potatoes in lightly salted water until tender, about 15–20 minutes. Drain well. Transfer the potatoes into a pan and cook on high heat for a minute to evaporate any excess moisture.

Mash the potatoes until smooth. Add the eggs, egg whites and just enough broth to moisten the mixture. (The amount of broth necessary will depend on the size of potatoes and how dry they are when you mash them.) Beat well. Add one tablespoon of oil and season with salt and pepper. The mixture should be firm enough to pipe through a pastry bag.

In a nonstick skillet, sauté the mushrooms and onions in the oil on medium-high heat until nicely browned, about 8–10 minutes. If necessary, add a little broth to prevent sticking or burning. Season with salt, pepper and thyme.

Line a baking sheet with foil and spray with nonstick spray (or line the pan with parchment paper).

Transfer the potato mixture into a large pastry bag fitted with a large star tube. Pipe the potatoes into mounds onto the prepared baking sheet, leaving a two-inch opening in the center of each mound. Spoon in some of the mushroom filling and sprinkle lightly with paprika. (This part can be prepared ahead of time, keeping the prepared potatoes in the refrigerator until you are ready to bake them.)

Bake, uncovered, in an oven preheated to 400 degrees Fahrenheit for 20 minutes, until golden.