Put the potatoes in a small saucepan, and add just enough water to cover them. Bring to a boil, and cook until the potatoes are tender, about 10 minutes. Drain through a sieve, and shake all the remaining water off. Return the potatoes to the saucepan, and add 2 tablespoons of the oil, nutritional yeast and 1/2 teaspoon salt. Mash with a fork until roughly smooth (it's OK if there are a few lumps). Set aside.
Heat the remaining 2 tablespoons oil in a small skillet over medium-high heat; add the shallots and a pinch of salt, and cook, stirring frequently, until soft and just starting to brown, about 3 minutes. Add the vinegar, tomato paste, paprika and cayenne and cook, stirring constantly, until the spices are toasted and the oil turns brick red, about 1 minute. Remove from the heat, and scrape every last bit into the mashed potatoes. Add half the parsley and peppers, the olives and 3/4 teaspoon salt, and stir to combine. (The filling can be made and refrigerated up to a day in advance.)
Preheat the oven to 425 F. Arrange the phyllo cups on a baking sheet, and fill each with a heaping teaspoon of the potato mixture. Bake until the filling is hot, 4 to 5 minutes. Garnish with the remaining parsley and peppers.
Copyright 2014 Television Food Network, G.P. All rights reserved.