For dressing: Place all ingredients into a small bowl and whisk together. Cover and refrigerate until ready to use.
For patties: Place all ingredients into a large mixing bowl and stir together until thoroughly combined. Cover and refrigerate for at least 2 hours. Divide mixture into four equal amounts and form into patties.
Pour half of oil into a cast iron skillet or nonstick pan and place over medium-high heat. Add patties, two at a time and sear for 4 to 5 minutes.
Flip patties and continue to cook for 3 to 4 minutes. Add cheese to each patty, 1 to 2 teaspoons of water and cover with lid for 30 seconds to 1 minute or until cheese melts. Remove cooked patties and repeat with remaining patties.
To assemble: Spread dressing onto each bun and top with quinoa patty. Add Top with lettuce, pickles and finally the bun tops. Gently press and serve.