Rinse the chicken thighs and pat dry. Cut each thigh in half. Season the pieces with 1/2 teaspoon of the salt and 1/4 teaspoon of the pepper.
Heat the oil in a large Dutch oven or skillet over medium-high heat. Add the chicken and cook until browned, about 5 minutes per side. Transfer to a plate. Add the onion, carrots, and garlic and cook for 1 minute. Pour in the broth and cook, stirring and scraping the bottom of the pan, for 1 minute. Add the cinnamon, ginger, and the remaining salt and pepper. Bring to a boil. Remove from heat and whisk in the yogurt. Stir in the raisins, almonds, rice, and browned chicken. Transfer to an oiled 8-by-11-inch baking dish or 2-quart casserole.
If using the phyllo, butter the tops of 6 sheets, stack them on top of one another, and place on the casserole, molding to fit. If not using the phyllo, cover the casserole with foil. Bake until golden, 25 to 30 minutes.