Melt the butter in a large saucepan. Add in the ham and cook in the butter until browned, about 5 minutes.
Add the onions into the pot and cook until golden brown, about 8 minutes. Add the carrots and celery and cook for 5 minutes.
Add the remaining ingredients to the pot and bring to a simmer. Cook for 1 1/2 hours or until the peas are very soft and breaking apart. Season to taste with salt and pepper.