Heat 1 teaspoon oil in a Dutch oven over medium-high heat. Add shallots; sauté 5 minutes or until tender and golden brown. Add curry powder; sauté 1 minute. Spoon shallot mixture into a large bowl.
Place 1/3 cup flour in a shallow bowl or pie plate. Dredge chicken in flour, shaking off excess. Heat remaining 1 tablespoon oil in pan over medium-high heat. Add half of chicken mixture; sprinkle with 1/4 teaspoon salt and 1/8 teaspoon pepper. Cook 6 minutes, browning on all sides. Add browned chicken to shallot mixture. Repeat procedure with remaining chicken mixture, 1/4 teaspoon salt, and 1/8 teaspoon pepper.
Add cider to pan, scraping pan to loosen browned bits. Combine 1 cup broth and 1 tablespoon flour, stirring with a whisk until smooth. Add broth mixture, remaining broth, and water; bring to a boil. Stir in chicken mixture, remaining 1/2 teaspoon salt, and remaining 1/4 teaspoon pepper. Cover, reduce heat, and simmer 40 minutes, stirring occasionally.
Stir in squash. Simmer, uncovered, 55 minutes or until chicken and squash are very tender and sauce thickens. Spoon about 1 cup stew into each of 6 bowls; sprinkle each serving with 2 teaspoons almonds and parsley, if desired.