Heat oil in a large nonstick skillet over medium-high heat. Add mushrooms, ginger, garlic, and jalapeño; stir-fry 2 minutes. Add edamame; stir-fry 1 minute. Stir in the corn, soy milk, and vinegar; cook until liquid almost evaporates (about 3 minutes). Remove from heat, and stir in cherries, salt, and white pepper.
Spoon the edamame mixture into the center of a large platter; arrange the cucumber and tomato slices alternately around mixture. Garnish with sesame seeds, if desired.