Soak fava beans overnight, at least 12 hours. Remove the shells.
Boil fava beans for 10-15 minutes, until soft, then drain and set aside.
Preheat the oven to 375º and line a baking sheet with parchment.
Heat 2 Tablespoons of oil in a skillet over medium heat. Sauté the shallot for 3 to 5 minutes, then add kale and peas, 1/2 Tablespoon of vinegar, and about 2 Tablespoons of water. Sauté for 5 minutes, or until kale looks wilted and tender.
In a food processor, give the sautéed mixture a few quick pulses. Do not over-process; this adds texture to your burgers! Empty the mixture into a large bowl.
Next, blend the fava beans with about 1 Tablespoon of olive oil in the food processor until smooth.
Add the pureed beans to the bowl, 1 teaspoon of sea salt, 1 Tablespoon of chickpea flour, and 1 1/2 Tablespoons of olive oil. Use a spoon to mix until well-combined.
Use 1/4 cup as your guide and shape the mixture into patties, placing them onto the baking sheet as you go. You will end up with 7 or 8 total.
Bake for 30-35 minutes, flipping halfway.