Of all batter‐fried foods, tempura is the lightest and easiest to make. Serve immediately; like many fried foods, it's best eaten standing up, around the stove. But it will hold in a low oven for a few minutes. You'll note from the variations that Japan is not the only country to serve batter‐fried vegetables as a light dish.
Put enough oil to come to a depth of at least 3 to 4 inches in a large, deep saucepan. The broader the saucepan, the more of these you can cook at once, but the more oil you will use. Turn the heat to medium‐high; you want the temperature to be at about 375°F when you start cooking. Combine the next five ingredients and set aside as dipping sauce.
Prepare the vegetables: Peel the broccoli and break it into florets; wash the zucchini and/or eggplant and slice it thin; peel and seed the winter squash and slice it thin; clean the mushrooms, then cut them into quarters if they're large; stem and seed the pepper and cut it into strips; trim and wash the string beans; and so on. Dry all vegetables well.
Combine the egg yolk and ice water in another bowl and beat well. Mix in 1 cup of the flour, just until blended. Don't worry about a few remaining lumps.
One piece at a time, dredge the vegetables and shrimp (if you are using) in the remaining flour, then dip in the batter. Fry each piece until golden, turning once if necessary, less than 5 minutes total. Drain on paper towels and serve immediately, with the dipping sauce.