Soak the chia seeds in the lime juice for at least 5 minutes.
Place the walnuts in a food processor and process into fine crumbs. Set walnuts aside. Place the toasted bread in the food processor and process into find crumbs. Set bread crumbs aside.
Place the garlic and shallots in a food processor and pulse to finely chop (be careful not to over process.) Remove the garlic and shallots from the food processor. Place the carrots in the food processor and pulse to finely chop (again, be careful not to over process.) Remove the carrots.
Heat the oil in a large heavy skillet over medium-heat; add the shallots and sauté for 3 or 4 minutes. Add the carrots and sauté for 3 or 4 minutes, or until the shallots and carrots are both tender. Transfer the shallots and carrots to a large mixing bowl.
Add the beans to the bowl with the sautéed vegetables. Use a potato masher to mash the beans in with the vegetables (you can also use your clean hands to make the job a little easier.) Add in the lime-soaked chia seeds, walnut crumbs, bread crumbs, salt and cumin. Use your clean hands to mix the ingredients together. Form six ½-cup patties with your hands.
Lightly rub the “dirty” skillet with oil and heat the skillet over medium heat. Working in batches, fry the patties 3-4 minutes per side. Transfer to a paper towel or place in a 200 degree oven to keep warm. Serve warm.