Place the macaroni, milk, chicken broth, butter, salt, and pepper in a large pot. Stir to combine.
Bring the mixture to a gentle simmer over medium heat. Cook for 10 to 12 minutes, stirring often, until the pasta is tender and most of the liquid has been absorbed.
Remove the pot from the heat. Add the shredded cheddar cheese a handful at a time, stirring until fully melted and the sauce is smooth.
Stir in the diced ham and frozen peas. Cover the pot and let it sit for 2 minutes so the ham and peas warm through.
Give the mixture one final stir and serve right away.