Combine first 14 ingredients in an electric slow cooker.
Cover with lid and cook on high setting for 4 hours or until carrot is tender.
Combine the water and cornstarch in a small bowl, stirring with a whisk until blended.
Add cornstarch mixture and frozen peas or edamame (and tofu, if using) to the slow cooker, stir well.
Re-cover and cook on high-heat setting an 30 additional minutes.
Serve with hot cooked rice.
Note: I don't eat much meat and prefer more vegetables, so I often add extra firm cubed tofu at the last 30 minute mark. Tasty! Also good with small new potatoes added at the beginning, which is another good way to stretch the recipe. :).