1. Prepare the Curry Sauce:

1. Sauté the Aromatics: Heat the vegetable oil in a large pot over medium heat. Add the chopped onions and sauté for about 5 minutes, or until they turn translucent. Add the minced garlic and grated ginger, cooking for another minute until fragrant.
2. Add Vegetables: Toss in the sliced carrot and diced potato (if using). Cook for another 3-4 minutes, stirring occasionally, to let the vegetables soften a bit.
3. Add Curry Powder: Stir in the curry powder, soy sauce, miso paste (if using), and sugar. Mix well to coat the vegetables in the spices, and cook for 2-3 minutes, allowing the flavors to bloom.
4. Add Broth: Pour in the vegetable broth, stirring to combine. Bring the mixture to a boil, then lower the heat and let it simmer for 10-15 minutes until the vegetables are tender and the sauce has thickened slightly. If you want a richer sauce, you can simmer it a bit longer.

2. Cook the Udon:

1. Boil the Noodles: In a separate pot, bring 4 cups of water to a boil. Add the udon noodles and cook according to package instructions (usually about 2-3 minutes for fresh noodles). Drain and set aside.
2. Season the Noodles: Once the noodles are drained, drizzle them with soy sauce and sesame oil (if using), giving them a quick toss to season evenly.

3. Combine the Curry and Udon:

1. Add Noodles to Curry: Once the curry sauce is ready, add the cooked udon noodles directly into the pot with the curry sauce. Stir to combine, making sure the noodles are well-coated with the sauce. Let everything simmer together for an additional 2-3 minutes so the flavors meld.

4. Serve and Add Toppings:

1. Plate the Dish: Ladle the curry udon into bowls. Top with your choice of toppings, such as chopped green onions, a soft-boiled egg, shredded nori, or a sprinkle of sesame seeds for added flavor and texture.