Preheat oven to 350°F. Line an 8 x 8-inch baking dish with parchment paper and lightly spray the parchment with nonstick cooking spray.
Spread the finely chopped macadamia nuts and uncooked quinoa in a single layer on a baking sheet. Bake until the quinoa is light golden, about 9 minutes.
Add the unsweetened coconut flakes to the same baking sheet and bake an additional 2–3 minutes, watching carefully so the coconut does not burn. Remove the baking sheet and let the toasted mixture cool slightly.
Drain and rinse the ⅔ cup chickpeas (128 grams). Pat them dry with paper towels to remove excess moisture.
Gently press each chickpea between your fingers to slip off and discard the skins, then place the skinned chickpeas into a large bowl.
Using a fork, mash the chickpeas in the bowl until as smooth as you can get them.
Add the toasted macadamia/quinoa/coconut mixture, the finely chopped dried pineapple, ¼ cup vanilla whey protein powder, ¼ teaspoon salt, ¼ cup white chocolate chips, and the zest of 1 large lime to the mashed chickpeas. Stir until evenly combined (using your hands to press and mix can help).
In a medium microwave-safe bowl, combine ⅓ cup honey and 1 tablespoon coconut oil. Microwave until the oil and honey are melted and bubbly, about 1 minute, then stir to combine.
Stir the warmed honey–coconut oil mixture and 1 large egg white into the chickpea–quinoa mixture until well combined.
Transfer the mixture to the prepared 8 x 8-inch pan and press it firmly and evenly into the pan.
Reduce the oven temperature to 300°F and bake the bars for 40–45 minutes, until the top is golden brown and feels firm to the touch.
Let the bars cool completely in the pan on a wire rack before removing the parchment and slicing into bars.