Rinse the chicken and pat it dry. Beat the eggs in a 9 by 13-inch dish. Lay the chicken pieces in the dish, and sprinkle with salt, pepper, and garlic powder. Turn the chicken and season the other side, then slosh the chicken parts around in the egg until well coated.
Put enough shortening or oil in a cast iron pan or electric skillet to come just halfway up the sides of the chicken parts. Heat the shortening or oil just until smoking, about 375 degrees F. Put the flour in a paper bag, add the chicken pieces, a few at a time, and shake to coat well. Remove the chicken with tongs and place it in the hot fat. Cover the pan, leaving a crack for steam to escape, lower the heat to 325 degrees F for electric skillet, and cook for 10 minutes. Turn the chicken with tongs, cover again (leaving the lid open just a crack), and cook for 10 minutes longer. Very large pieces may need to be cooked a little longer. Drain the chicken on paper towels and transfer to a platter.
To make the glaze, melt the butter in a saucepan over low heat. Whisk in the honey until well blended. Bring to a simmer and add the pecans. Simmer for 10 minutes, stirring occasionally. Ladle the glaze over the hot fried chicken and serve.