Prepare the Curry Broth

1. Heat vegetable oil in a large pot over medium heat. Add sliced onions and cook until softened and translucent, about 5-7 minutes.
2. Add minced garlic and grated ginger, cooking for another minute until fragrant.
3. Sprinkle flour over the onions and stir constantly for 2 minutes to create a roux base.
4. Gradually whisk in dashi stock, making sure no lumps form.
5. Add carrots, curry powder, soy sauce, mirin, and honey. Bring to a simmer and cook for 15-20 minutes until carrots are tender and broth has thickened.

Make the Chicken Katsu

1. Place chicken breasts between two pieces of plastic wrap and pound to ½-inch thickness using a meat mallet or rolling pin.
2. Season both sides with salt and pepper.
3. Set up three shallow bowls: one with flour, one with beaten eggs, and one with panko breadcrumbs.
4. Dredge each chicken breast in flour, then egg, then press firmly into panko to coat completely.
5. Heat 1 inch of vegetable oil in a large skillet to 350°F. Fry chicken for 4-5 minutes per side until golden brown and cooked through.
6. Drain on a wire rack and let rest for 3 minutes before slicing.

Cook Udon Noodles and Assemble

1. Cook udon noodles according to package directions. Fresh udon typically takes 3-4 minutes in boiling water.
2. Divide cooked udon noodles between bowls.
3. Ladle hot curry broth over noodles.
4. Top with sliced chicken katsu, soft-boiled egg (if using), and garnish with green onions and beni shoga.