Bring a large pot of salted water to a boil. Meanwhile, dice 8 ounces cooked ham (1 1/3 cups). Dice 14 to 16 ounces cooked boneless chicken (3 cups). Place 1 can condensed cream of chicken soup, 1 cup half-and-half, 2 tablespoons Dijon mustard, 2 teaspoons fresh thyme leaves, 1/2 teaspoon cayenne pepper, 1/2 teaspoon kosher salt, and 1/4 teaspoon black pepper in a medium bowl and whisk to combine. Grate 1 pound Gruyère on the large holes of a box grater (4 cups).