Preheat the oven to 425°F.

Season each chicken thigh with about 1 teaspoon salt (make sure to sprinkle the salt on all sides of the chicken) and a pinch of pepper. Arrange the chicken on a baking sheet, skin side up, and roast until the chicken is golden brown and very tender when pierced with a knife (the internal temperature should be about 175°F), 45 to 60 minutes, depending on the size of the pieces. Remove the chicken from the oven and set aside to cool for about 25 minutes.

Reduce the oven temperature to 400°F. 

While the chicken is cooking, fry the eggplant: Place the eggplant slices on a wire rack and sprinkle them on both sides with salt, about 2 tablespoons total. Set the eggplant aside for about 30 minutes to draw out the juices.

Pat the eggplant slices dry with a paper towel. Line a baking sheet with paper towels.

Heat ⅓ cup olive oil in a large skillet over medium-high heat. Once the oil is hot, carefully add 4 eggplant slices, or as many as will fit comfortably without crowding, to the pan. Fry, turning once, until deep golden brown on both sides, 5 to 8 minutes per side. Transfer the fried eggplant to the paper towel-lined baking sheet. Continue frying the rest of the eggplant in batches, adding more oil to the pan and adjusting the heat as needed. If the fried eggplant slices look oily, blot the top surface with paper towels. Set the eggplant aside.

Heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add the onions and cook, stirring occasionally, until soft and golden brown, 20 to 25 minutes. Add 1 1/2 teaspoons salt and the honey to the onions and stir to combine. Remove from the heat and set aside.

Once the chicken is cool enough to handle, pull the meat from the bones and shred it using two forks, aiming for bite-sized pieces. Cut or shred the skin as well (discard the bones). Put the shredded chicken and skin in a medium bowl. Add the cumin, nutmeg, and cinnamon and mix well to combine. Taste and add more salt and pepper as needed. Set aside.

Assemble the almoronia: Arrange about half the eggplant in a 9-by-13-inch baking dish in an even layer, overlapping the slices as needed to fit. Spread half the shredded chicken over the eggplant in another even layer. Set aside about one-quarter of the caramelized onions and spread the rest over the chicken. Spread the remaining chicken into a layer on top of the onions, and top with the remaining eggplant pieces. Press gently to lightly compact the layers and make the almoronia easier to cut and serve, then distribute the reserved onions over the top.

Bake the almoronia, uncovered, until all the ingredients are hot, about 30 minutes. Remove from the oven.

To serve, scoop out portions, making sure to get a bit of each layer in each one, and arrange on plates.