In a large skillet, heat 1-teaspoon olive oil. Add the spinach, using tongs to toss, cook until wilted, about 2 minutes. Transfer spinach to a sieve, using wooden spoon press spinach to remove as much liquid as possible. Allow cool, then chopping and transferring to a large bowl. Set aside.
In the same pan, heat the remaining 2 tablespoons olive oil over medium heat. Add the onion and cook, stirring occasionally, until brown around the edges, about 5 minutes. Add the garlic and cook until fragrant, less than a minute. Add the broth and freekeh and bring to a boil. Cover pan, reduce the heat to medium low, and cook until the freekeh is tender and the broth is absorbed, about 15 minutes. When the freekeh has finished cooking, remove from heat and allow to cool for 10 minutes uncovered.
In the large bowl with the spinach, add the cooked freekah, chickpeas, panko, parsley, pine nuts, lemon juice, zest, cumin, and coriander. Using a potato masher, mash mixture until the chickpeas are mashed and sticky but still a little chunky. Season with salt and pepper to taste. Stir in the egg. Chill the chickpea mixture for at least 30 minutes or up to 4 hours.
Portion the chickpea mixture into 8 balls. With moist hands, form balls into patties about ¾ inch thick.
In a large skillet or cast-iron pan, heat the canola oil over medium heat. Add the burgers, reduce heat to medium low, and cook until browned on one side. Gently flip with a thin spatula and cook until browned and heated through, about 3 to 4 minutes.
Serve burgers on grilled pita bread with tzatziki.