Smothered Potato Latkes

Name: Smothered Potato Latkes
Ingredients: 2 tablespoons extra-virgin olive oil, divided; 2 small onions, 1 thinly sliced and 1 quartered, divided; 2 tablespoons water; 8 ounces white mushrooms, quartered; 1 ½ teaspoons salt, divided; ¾ teaspoon ground pepper, divided; 1 ½ cups shredded Braised Brisket with Tomatoes & Onions (See Associated Recipe); 2 ½ pounds russet potatoes, peeled; 2 large eggs, separated; 1 tablespoon matzo meal; 1 cup canola or grapeseed oil; Chopped fresh chives for garnish