For garlic mayo: Combine all ingredients and refrigerate for at least 30 min. before using as a burger spread. (Tip: To make the garlic mayo into a creamy dressing, whisk in milk or buttermilk until desired consistency is reached and adjust seasoning to taste.)
For burgers: Combine quinoa and water in a medium saucepan. Bring to a boil then reduce heat to low, cover, and cook for 15 min. or until water is absorbed. Remove from heat, uncover, fluff with a fork, and let cool slightly. Place half of the cooked quinoa in a food processor. Add beans and 2 Tbsp. of the oil. Pulse several times just until mixture starts to become paste-like. In a large bowl, mix quinoa-bean paste with remaining quinoa, egg, bread crumbs, carrot, onion, parsley, and seasoning. Cover and refrigerate at least 30 min. or up to overnight.
Heat 2 Tbsp. olive oil in a large, nonstick skillet over medium heat. Form quinoa mixture into 4 equal balls and press balls into 3/4-inch to 1-inch thick patties. (Tip: If burger mixture is too crumbly to stick together in a patty, add 1 to 2 Tbsp. water to the mix.) Sear patties for 7 to 10 min. per side or until browned and firm on the outside. Be sure the first side of the quinoa burger is well browned and firm before turning burgers over in the pan; this will make them easier to flip. (Tip: Keep heat at medium so olive oil doesn’t burn. Patties will end up soaking up a lot of the oil in the pan, which is okay; this helps them crisp on the outside and you won't need to add more oil.)
Divide greens among 4 plates. Set each burger on top of a plate of greens. Spread burgers with garlic mayo then top with Apple-Carrot Quick Pickle.