Heat butter in a small skillet over medium heat. Add carrots and sauté for about 2 minutes or until carrots begin to soften. Add peas and sauté for another minute.

Remove carrots and peas from heat and add to a large bowl. Add minced chicken, mashed potato, onion powder, and nutmeg. Season with salt and pepper and mix until combined. Add egg and 2 tablespoons flour and mix until combined. If mixture seems too wet add another tablespoon of flour. Cover mixture and chill.

While mixture is chilling make the gravy dipping sauce. Melt the butter in a small saucepan and sauté the shallots over medium-low heat for about 5 minutes or until translucent. Add the flour and cook over low heat, stirring constantly for about 2 minutes. Add 1 cup chicken broth to the sauce and whisk over low heat until thickened, about 1-2 minutes. For a thinner sauce add another 1/2 cup of broth. Add heavy cream, garlic powder and nutmeg. Season with salt and pepper. Set aside.

Place flour, eggs and panko into three separate shallow bowls. Divide the croquettes into 16 equal portions and form into balls (I used a small cookie scoop for this part). Coat each croquette in flour, then eggs, followed by panko.

Heat oven to 200°. In a large skillet, heat 1/2 inch of canola oil until shimmering but not smoking. Fry croquettes in batches, turning as necessary until all sides are golden brown, about 3 minutes. Transfer the croquettes to a wire rack set over a baking sheet and place in oven to keep warm while frying the remaining croquettes. Sprinkle with salt and serve immediately with warm dipping sauce.