Preheat the broiler to high heat.
Melt the butter in a large ovenproof skillet over medium heat. Add the onions and cook until softened, about 3 minutes. Add the ham and thyme and continue to cook until the ham is lightly browned.
Add the chicken broth and 3/4 cup water and bring to a simmer. Add the gnocchi, stir well, cover and cook until the gnocchi is slightly tender, about 5 minutes. Remove from the heat. Uncover and stir in the peas, cream, 1/4 teaspoon salt and 1/4 teaspoon pepper. Sprinkle the cheese over the top and broil until golden and bubbly, about 3 minutes. Serve.