Step 1

Bring water to a boil in a small saucepan. Add quinoa and return to a boil. Reduce to a low simmer, cover and cook until the water has been absorbed, about 10 minutes. Uncover and let stand.

Step 2

Heat 1 tablespoon oil in a medium skillet over medium heat. Add 1/2 cup onion and garlic and cook, stirring occasionally, until soft and fragrant, about 3 minutes. Add beans, paprika and ground cumin and mash the beans to a smooth paste with a potato masher or fork. Transfer the mixture to a bowl and let cool slightly. Add the quinoa, 3 tablespoons cilantro, 3 tablespoons cornmeal, 1/2 teaspoon salt and pepper; stir to combine.

Step 3

Form the bean mash into 6 patties. Coat them evenly with the remaining 1/3 cup cornmeal and transfer to a baking sheet. Refrigerate for 20 minutes.

Step 4

To prepare guacamole: Mash avocado with a potato masher or fork. Stir in 2 tablespoons cilantro, lemon juice, 2 teaspoons onion, garlic, cayenne and 1/8 teaspoon salt.

Step 5

Preheat oven to 200 degrees F.

Step 6

Heat 1 tablespoon oil in a large cast-iron (or similar heavy) skillet over medium-high heat. Reduce heat to medium and cook 3 burgers until heated through and brown and crisp on both sides, 2 to 4 minutes per side. Transfer to the oven to keep warm. Cook the remaining 3 burgers with the remaining 1 tablespoon oil, reducing the heat as necessary to prevent overbrowning. Serve the burgers on buns with lettuce, tomato and the guacamole.