Start the oven: Heat the oven to 425°F. Line a sheet pan with parchment paper so the chickpea patties release easily.

Cook the quinoa: Put the rinsed quinoa, 1 3/4 cups water, and 1/2 teaspoon of the salt into a small saucepan. Set the pan over high heat and bring the water to a boil.

Cover the saucepan, turn the heat to low, and cook the quinoa for 15 minutes. The water should be absorbed and the grains should look tender.

Take the saucepan off the heat and let the quinoa sit, still covered, for 5 minutes. This finishes the steaming without drying it out.

Make the chickpea patties: Put the dried chickpeas into a medium bowl. Mash them with a potato masher or a fork until most of the beans are broken up and the mixture looks chunky but can still hold together.

Add the finely chopped red onion, half of the parsley, the cumin, the panko, and 1/2 teaspoon of the salt to the bowl. Mix well so the seasonings are spread through the chickpeas.

Crack the egg into a small bowl and beat it with a fork until the yolk and white are combined. Pour the egg into the chickpea mixture and stir until the mixture holds together when you press it in your hand.

Divide the chickpea mixture into 8 small patties and place them on the prepared sheet pan. Brush or drizzle 1 tablespoon of the olive oil over the tops.

Put the sheet pan in the oven and bake the patties for 10 minutes. The bottoms should start to dry and lightly brown.

Flip the patties carefully with a thin spatula. Bake them for 8 to 10 minutes more, until both sides are browned and the edges feel firm.

Build the salad and sauce: While the patties bake, put the sliced red onion, chopped cucumber, halved grape tomatoes, and the remaining parsley into a large bowl.

Squeeze in the juice from half of the lemon. Add the remaining 1 tablespoon olive oil and 1/4 teaspoon salt, then toss the salad until everything is evenly coated.