Heat a gas grill to medium high or prepare a medium-hot charcoal fire. Remove the thick, outer leaves of the corn husk. Peel back the inner leaves, being careful to leave them attached to the cob. Remove as much of the corn silk as possible and then fold the inner leaves back over the corn. It’s fine if some of the kernels show through gaps in the leaves.
Once the fire is hot, put the corn on the grate, cover the grill, and cook, flipping often, until the husk is very charred and some of the kernels are browned and feel cooked when pressed with a fingernail, 10 to 15 minutes. Set aside to cool.
Combine the shallot, Champagne or white-wine vinegar, and sherry vinegar in a medium bowl. Season with salt and pepper and let macerate for 20 minutes. Whisk in the oil. Taste and adjust the seasonings; set aside.
Meanwhile, wash and dry the arugula. Put it in a bowl, cover with a damp paper towel, and refrigerate.
Shuck the corn and wipe it off well, making sure no flecks of charred husk or corn silk cling to it. Cut the kernels off the cob and put them in a large salad bowl. Cut each cherry tomato in half from stem to tip and set aside (don’t refrigerate).
To assemble the salad: Pour some of the the vinaigrette over the corn and toss well. Gently toss in the arugula and tomatoes, drizzle with the remaining vinaigrette, and season with a little salt and pepper. Crumble the ricotta salata over the salad and serve.