Place eggplant slices and cubes in a colander, sprinkle with salt and drain for 20 minutes.
In a mini food processor, combine garlic, saffron, and parsley. Pulse to make a paste. Set aside.
Insure that the Paella pan (15-17") will fit into the oven and preheat oven to 425 F.
Dry the eggplant with paper towels. On a parchment lined baking sheet arrange the eggplant in a single layer. Drizzle with 4 tablespoons of extra virgin olive oil. Sprinkle with some freshly ground black pepper. Bake for about 20-30 minutes or until tender. Remove to a plate and set aside.
In the Paella pan, heat 3-4 tablespoons of olive oil over medium high heat, add the chicken pieces and sauté just until chicken is no longer pink. (chicken should not be fully cooked). Reserve chicken to a platter and cover with foil.
Add more olive oil if Paella pan is too dry, add the onion, red peppers, thyme, and bay leaves. Cook over medium high heat until tender.
Add the tomatoes and increase heat to high until liquid has evaporated. Add the wine and reduce until almost no liquid remains.
Reduce the heat to medium low and add the eggplant cubes and Chorizo slices, stirring cook for about 2 minutes. Remove the bay leaves.
Add the rice and stir well to coat rice and combine ingredients.
Add the hot chicken broth and saffron mixture and bring to a boil. Adjust for salt.
Stir and continue to boil until the rice mixture is no longer soupy, about 5 minutes.
Stir in the chicken pieces and arrange eggplant slices over the rice. Do not stir at this point. Cover with foil and cook until rice is al dente about 15-20 minutes. Or, bake in oven uncovered for about 15-20 minutes.
Remove from heat and let rest for 5-10 minutes. Garnish with chopped parsley.