In a large bowl, stir together the quinoa, eggs, spinach, feta, chives and 1/4 tsp. salt. Form the quinoa mixture into 8 patties. In a large nonstick skillet cook 4 patties in 1 Tbs. hot oil over medium-high heat until golden brown on each side, about 6 minutes total. Repeat with remaining patties and 1 Tbs. oil.
In a medium bowl combine the tomatoes, cucumber, arugula, 1 Tbs. oil, and 1/8 tsp. salt. Serve with the quinoa patties.