Pierce potato with a fork; place on paper towels in microwave oven. Microwave at high 5 minutes or until fork pierces potato easily, turning potato after 3 minutes. Wrap in a towel; let stand 5 minutes. Peel and mash potato.
Bring 2 cups water to a boil in a saucepan; add quinoa and salt. Cook 15 minutes; drain.
Heat 1 teaspoon oil in a large nonstick skillet over medium-high heat. Add onions, cilantro, and jalapeño; sauté 1 minute. Add cumin, oregano, black pepper, and garlic; sauté 1 minute. Combine potato, quinoa, onion mixture, cottage cheese, and cheddar cheese in a bowl, stirring well. Let stand 5 minutes; stir in egg.
Shape potato mixture into 10 patties. Carefully dredge each patty in panko. Place on a baking sheet. Cover and chill 10 minutes.
Heat 1 1/2 teaspoons oil in skillet over medium heat. Add 5 patties to pan; cook 2 minutes on each side or until golden brown. Keep warm. Repeat procedure with remaining oil and patties.