Heat 2 teaspoons oil in a skillet over medium heat. Add vegan burger patties; cook, flipping halfway, until browned, about 6 minutes. Transfer to a plate and cut into bite-sized cubes.
Heat remaining oil in a pot over medium-high heat. Add onion, garlic, chipotle pepper, salt, and pepper. Saute until onion is translucent, about 5 minutes. Add 1 cup vegetable stock and tomato paste; bring to a simmer. Add the browned vegan patties and plum tomatoes with juice.
Pour remaining vegetable stock into the tomato mixture. Sprinkle in adobo seasoning and sazon. Bring to a boil. Add potatoes and kale; cook until potatoes are tender, 10 to 15 minutes.