Preheat oven to 350°. In a medium bowl, combine chia seeds and 1 1/2 tbsp. water; set aside. Cook quinoa according to package instructions, about 15 minutes.
Meanwhile, sauté onion in 1 tbsp. oil in a medium frying pan over medium-high heat until starting to brown, about 5 minutes. Add spinach and artichokes and cook until spinach wilts, about 2 minutes. Pour into bowl with chia seeds and mix well. Drain quinoa and add to bowl. Stir in bread crumbs, salt, pepper, and parmesan.
Rub 5 ramekins (4- to 4 1/2-oz. size) with remaining 1/2 tbsp. oil and set on a rimmed baking sheet. Divide quinoa mixture among ramekins. Press with fingers to compact mixture so ramekins are filled two-thirds. Bake until cakes are lightly browned on top, about 30 minutes. Let cool completely.
Remove quinoa cakes from ramekins with a small spatula. Wrap each cake in foil or waxed paper.
Make ahead: Chilled, up to 1 week. In a backpack, 1 day.
*Find in the baking aisle at well-stocked supermarkets.