In a large bowl, whisk together the flour, ice cold water, beaten egg, baking soda, and salt to make the tempura batter. Set aside.
Heat vegetable oil in a large pot or deep fryer to 375°F (190°C).
Dip the shrimp, sweet potato slices, zucchini slices, and broccoli florets into the tempura batter, coating them evenly.
Carefully place the battered shrimp and vegetables into the hot oil and fry until golden brown and crispy, about 2-3 minutes. Remove with a slotted spoon and transfer to a paper towel-lined plate to drain excess oil.
Meanwhile, cook the udon noodles according to package instructions. Drain and set aside.
In a separate pot, heat the vegetable broth over medium heat. Stir in the soy sauce, mirin, minced garlic, and grated ginger. Bring to a boil and simmer for 5 minutes.
Divide the cooked udon noodles among serving bowls.
Pour the hot broth over the noodles. Top with the fried shrimp and vegetables.
Garnish with sliced green onions and drizzle with sesame oil.
Serve hot and enjoy!