1. Place potatoes in a medium-sized pot. Fill with water to cover and bring to a boil over medium-high heat. Boil until fork-tender, about 20 minutes. Drain potatoes and mash.
2. While potatoes are boiling, heat oil in a large frying pan. Add onions and sauté until golden, about 15 minutes. Add onions to mashed potatoes. Add in eggs, salt, pepper, and potato starch. Mix until well combined.
3. Preheat oven to 350 degrees Fahrenheit (180 degrees Celsius). Line two baking sheets with Gefen Parchment Paper.
4. Heat olive oil for the mushroom filling in a medium-sized frying pan. Add shallots to the pan and sauté over medium heat for 10 minutes, stirring occasionally. Add in garlic and mushrooms and stir for five minutes. Add in chicken broth, red wine vinegar, lemon juice, and thyme. Raise heat, stirring constantly until all the liquid is totally absorbed. Remove from heat and set aside.
5. Using a one- and- a- half-inch scoop, prepare 30 potato balls. Place three across each row on the baking sheets. Make an indentation in the center of each potato ball with your thumb and slightly enlarge the center. Fill each center with one teaspoon of the mushroom filling (recipe follows). Brush each thumbprint with the beaten egg. Bake for 30 minutes.