Steam the sweet potato cubes for 10 to 12 minutes until tender, then spread them on a plate to cool and release steam.
Mash the sweet potato coarsely and mix it with the quinoa, oats, egg, smoked paprika and salt.
Shape 4 compact patties and refrigerate them for 15 minutes until firm.
Blend the mayonnaise, parsley, scallions, lemon juice and capers until flecked green but not completely smooth.
Cook the patties in a lightly oiled nonstick skillet over medium heat for 5 to 6 minutes per side, flipping once, until browned and set.
Rest the patties for 3 minutes and toast the buns cut-side down.
Spread green goddess sauce over each bun and add lettuce and one sweet potato quinoa patty.