Cook onion, mushrooms, and garlic in 3 tablespoons hot oil in a large skillet over medium-high heat 10 minutes, stirring often.
Peel a strip around each potato with a vegetable peeler, if desired. Place potatoes in a 4 1/2-quart electric slow cooker. Add carrots; sprinkle with poultry seasoning and 1 1/2 teaspoons salt. Stir well.
Sprinkle remaining 1 teaspoon salt and 1/2 teaspoon pepper over chicken. Brown chicken in large skillet in 1 tablespoon oil. Remove chicken from skillet and place, browned side up, over vegetables in slow cooker.
Add wine to skillet, and cook 2 minutes, stirring to loosen particles from bottom of skillet. Pour wine over chicken. Sprinkle with remaining 1/2 teaspoon pepper. Cover and cook on HIGH 1 hour. Reduce to LOW, and cook 6 hours.
Combine flour and water, stirring until smooth. Add flour mixture and peas to slow cooker; stir gently. Cover and cook on LOW 5 more minutes. Serve fricassee over rice or noodles.