Toss 2 lb. mixed vegetables, such as 4x1/2-inch spears of English hothouse or Persian cucumbers, 4x1/4-inch spears of peeled carrots, and quartered radishes, with 1 1/2 tablespoons kosher salt in a large wide nonreactive bowl. Press plastic wrap on surface of vegetables. Place a small plate over, then weigh down with two 28-oz. cans (such as canned tomatoes). Let stand at room temperature for 2 hours.
Remove cans, plate, and plastic wrap; transfer vegetables to a colander. Rinse well with cold water. Transfer drained vegetables to a large bowl. Add 8 thinly sliced shiso or large basil leaves, 1 red Fresno chile or jalapeño cut into 1/2-inch rings, 3 tablespoons sake, 2 tablespoons seasoned rice vinegar, 2 teaspoons sesame seeds, and 1 teaspoons finely grated peeled ginger.
Toss to coat; cover and refrigerate, tossing occasionally, for at least 1 hour. DO AHEAD Pickles can be made 1 week ahead. Keep chilled, tossing occasionally.
To serve, use a slotted spoon to transfer vegetables from pickling liquid to large mugs, mason jars, or bowls.