Don't toss those stems! Rainbow chard is sold in bunches with a mix of yellow, pink, and pale green stems that add a pop of color, a bit of crunch, and an extra dose of fiber.
Preheat oven to 350 degrees F.
Fold chard leaves in half along stems; run a knife alongside the stems to remove the leaves. Chop the stems. Stack the leaves and coarsely chop. Set both aside separately.
Whisk together eggs, egg whites, salt, and pepper in a medium bowl; set aside.
Place potatoes in a large pot and add 1 cup water. Bring to a boil. Cover, reduce heat to low, and simmer until the potatoes are tender when pierced with a fork, 5 to 10 minutes. Drain.
Heat 1 Tbsp. oil in a 10-inch ovenproof nonstick skillet over medium-high heat. Add half of the potatoes to the pan; cook until browned, 2 to 3 minutes per side. Transfer to a large bowl. Repeat with the remaining potatoes.
Heat the remaining 1 Tbsp. oil in the pan. Add the chard stems, onion, and garlic. Cook, stirring, until tender, 4 to 6 minutes. Stir in the chard greens; cook until wilted, 1 to 2 minutes. Transfer to the bowl with the potatoes. Add chorizo to the pan; cook, crumbling with a spoon, until cooked through, 3 to 5 minutes. Transfer the chorizo to the bowl with the potato mixture and toss gently to combine.
Spoon the potato-chorizo mixture into the skillet. Pour the egg mixture over the top and sprinkle with cheese. Bake until the top is lightly browned and the center is set, about 25 minutes. Let cool for 15 minutes. Place a large plate on top of the pan. Protecting your hands with oven mitts, grasp both the pan and the plate together and invert, so that the tortilla falls onto the plate. Slide the tortilla onto a large cutting board; cut into 6 wedges to serve.