Step 1Scrub the potatoes (do not peel) and cut each into 3 to 4 pieces. Place the potatoes in a large microwaveable bowl with the boiling water. Cover the bowl with a microwaveable plate and cook on high for 15 minutes. Remove the soft potatoes and place them in a separate bowl. (If some pieces are not soft, return them to the microwave, cover and cook for an additional 3 minutes.)
Step 2While the potatoes are cooking, heat a saute pan over medium-high heat until hot. Add the 2 tablespoons of oil, then the red onion and saute until golden, stirring occasionally. Remove from heat and set aside.
Step 3Wait just until the softened potato pieces are cool enough to handle, then peel the warm pieces. Put the pieces through a ricer, or mash them.
Step 4To the potatoes, add the sauteed red onion, the green onions, the flour, feta cheese and egg. Mix the latke mixture well with a spoon, adding additional flour as needed to form a slightly tacky base. Season with 1 1/4 teaspoons salt and a heaping one-fourth teaspoon pepper, or to taste. Form the mixture into small latkes, about 2 1/2 inches in diameter.
Step 5Heat a thin film of oil in a large, nonstick frying pan over medium heat until hot. Fry the latkes, a few at a time, on each side until browned, about 2 minutes per side. Transfer the latkes to a paper towel-lined plate before serving.