In a small dry skillet over medium heat, toast the nuts until fragrant, about 5 minutes. Transfer to a cutting board to cool, then finely chop.
Using either a food processor with the large-holed grating attachment, or the large holes of a box grater, grate the apples and the carrot. You should get about 1 1/2 cups apple and 1 cup carrot.
In a large bowl, beat the eggs. Add the apple, carrot, flour, ginger, baking powder and salt and stir to combine.
In a large nonstick skillet or well seasoned cast-iron skillet over medium heat, heat 2 tablespoons of the oil until shimmering. Scoop a scant 1/4 cup of batter into the pan and tilt the pan around to spread the batter out, pressing with the bottom of the scoop after each mound is placed in the pan so that each pancake is about 3 1/2 inches in diameter. You should get 5 to 6 pancakes in the pan. Cook the pancakes until well browned and crisp on the outside and warmed through, about 3 minutes per side, then transfer to a plate. Repeat with the remaining oil and batter.
Divide the pancakes among 4 plates and top each serving with a dollop of yogurt and a sprinkle of walnuts.