Preheat your oven's broiler.
In a large oven safe skillet over medium heat, melt the butter to coat the pan.
Add the onion and mushrooms and cook until softened, mushrooms have lost their liquid and are browning, 8 to 10 minutes.
Add in the ham and the garlic and cook 30 seconds longer, until fragrant.
Whisk in the wine, scraping up and browned bits.
Stir in the chicken broth and gnocchi. Bring to a simmer, cover and cook for 5 to 8 minutes, stirring occasionally, until gnocchi is tender.
Remove from heat and stir in the peas and cream. Season with salt and pepper to taste.
Sprinkle the cheese over top and place in broiler to brown.
When cheese is melted, remove from oven and serve.