Heat 4 tablespoons of the oil in a large (12-inch), deep skillet over medium-high. Add the onions, garlic and carrots; fry, stirring often, until onions are crisp-tender but not brown, about 5 minutes. Stir in the mushrooms, broth, vinegar, thyme, marjoram, cinnamon stick, pepper, bay and cloves. Simmer, covered, over low heat, stirring occasionally, for 30 minutes. Remove from heat, add the jalapenos, and season with salt, usually about 1 teaspoon. Pour into a wide baking dish (a 13 x 9-inch glass baking dish works perfectly here).
Sprinkle both sides of the chicken liberally with salt. Wipe out the skillet, add the remaining 1 tablespoon of the oil and set over medium heat. When hot, lay in the chicken in an uncrowded layer. Cook, turning once, until browned and cooked through, about 4 minutes per side.
Transfer the chicken from the skillet to the baking dish, nestling the pieces into the escabeche (the brothy mixture should almost cover the chicken.) Let cool completely, about 1 hour; cover and refrigerate if not serving right away.
If using the optional green beans, add them to the escabeche. Taste and add more salt if necessary. If chilled, warm the dish to room temperature before serving. (You may want to remove the bay leaves, cloves and cinnamon if you’re looking for a less rustic presentation.) Garnish with sprigs of thyme and marjoram, if you have them.