For the croquettes, heat butter in a skillet over medium heat. Add onions and garlic, and season with salt, pepper, thyme, cayenne pepper, and nutmeg. Stir 5-6 minutes to soften, add flour and whisk 1 minute. Whisk in chicken stock then cream. Add some to a small bowl with the egg yolks to temper then add everything back to the sauce and let thicken. Remove from heat and stir in about 1/2 cup breadcrumbs – the sauce should be very thick. Let cool, then pour room temp sauce over cold chicken. Combine and chill at least 1 hour more.
Heat a few inches of oil in a Dutch oven or in a countertop fryer to 360°F to 365°F.
Heat oven to 275°F and place a wire rack in a rimmed baking sheet.
Combine remaining breadcrumbs with Panko, parsley and cheese in a shallow dish. Beat egg with water in a second shallow dish.
For the gravy, melt butter in a saucepot or skillet over medium to medium-high heat. Whisk in flour, cook 1-2 minutes, add stock and let thicken. Season with Worcestershire, salt and pepper. Ladle some gravy into egg yolk to temper then add back to gravy, adjust seasoning to taste and reduce heat to low.
Use a conical ice cream scoop to form a pyramid shape or use damp hands to roll balls and form 12-15 croquettes. Turn croquettes in egg wash then gently press breading mixture evenly all over the croquettes. Fry croquettes 3-4 at a time until deeply golden, turning conical shapes gently as they cook to evenly brown, 5-6 minutes per croquette.
Keep croquettes warm in oven on rack until ready to serve.