Bring 4 cups of salted water to a rolling boil in a large pot. Meanwhile, prepare an ice bath by combining the ice and a splash of cold water in a large mixing bowl.
Drop the trimmed green beans into the boiling water and blanch for 3 to 4 minutes until they are bright green and tender-crisp.
Immediately transfer the blanched green beans to the prepared ice bath using a slotted spoon or tongs. Let them cool completely for about 2 minutes to stop the cooking process.
Drain the green beans thoroughly and pat them dry with a clean kitchen towel or paper towels.
In a large serving bowl, whisk together the extra virgin olive oil, balsamic vinegar, minced garlic, kosher salt, and black pepper.
Add the dried green beans, halved red cherry tomatoes, and halved yellow cherry tomatoes to the bowl. Toss gently to coat the vegetables in the dressing.
Sprinkle the grated Parmesan cheese and torn fresh basil leaves over the top. Give the salad one final light toss before serving.