For the tempura batter: Combine 1 cup water and 1 cup ice, let sit. Cut vegetables in the meantime while ice cools water. Mix together eggs and flour, adding in 1 cup ice water. The batter should be somewhat lumpy and sticky.
Mix together dipping sauce and set aside.
Heat 1/2 cup canola or vegetable oil in a large pot on med-high heat for approx 3-4 min. Once hot, dip veggies in batter, then in panko breadcrumbs. Cook in batches in oil for about 2 min, turning halfway through cooking time. Set on paper towel to drain and season with salt.
Meanwhile, cut beef strips in half and roll around a pile of enoki mushrooms. Season with salt and pepper, and then drizzle rolls with soy sauce. Cook on med-high heat in 2 tbsp of olive oil for about 3 minutes.
Serve tempura and beef enoki rolls with dipping sauce and enjoy!