Bring a large pot of water to a boil for the pasta. Once boiling, add the pasta and cook for 8-10 minutes until tender. Add the frozen peas and continue to cook for one minute, then drain the pasta and peas in a colander.

While the pasta is cooking, dice the ham into small pieces. After draining the pasta and peas, add the diced ham and butter to the pot. Cook over medium heat, stirring often, until the ham has browned, about 5 minutes.

Add the drained pasta and peas back to the pot along with the heavy cream. Stir and heat over medium until the cream is hot, about 2-3 minutes, dissolving the browned bits off the bottom of the pot as you stir.

Remove the pot from the heat, sprinkle the grated Parmesan over the pasta, and stir to combine. Season to taste with salt and pepper, then serve.