Skirt Steak With Shallots and Sautéed Watercress

plus 1 teaspoon olive oil

large shallots, sliced

sprigs fresh thyme

Kosher salt and black pepper

red wine vinegar

unsalted butter

skirt steak, cut into 4 pieces

cremini mushrooms, stems trimmed and thinly sliced

bunches watercress, thick stems removed (about 6 cups)