Blanch the broccoli by filling a large bowl with ice water and bringing a large pot of salted water to a boil. Add the broccoli florets to the boiling water and cook until crisp tender, 1 minute. Drain and place the broccoli in the ice water to cool. (This stops the cooking, sets the bright green color of the broccoli and makes it much more pleasant to eat.) Drain really, really well.
Make the dressing by whisking together the mayonnaise, yogurt, Dijon mustard, whole-grain mustard, sherry vinegar, tarragon and salt and pepper to taste.
Add enough dressing to the warm chopped chicken to moisten it well. Add the broccoli and cherry tomatoes and mix gently to combine.
Cover with plastic wrap and refrigerate for a few hours, giving the flavors time to develop.
Remove from the refrigerator and allow to come to room temperature before serving.