Begin to boil water in a large pot for the tortellini.
Melt butter in a large skillet over medium-high heat. Add garlic and mushrooms and cook until tender.
Add cream, ham, and salt, bring to a boil, reduce heat and allow mixture to simmer for about 5 minutes until thickened.
Meanwhile, cook the tortellini according to directions on package and toss in frozen the peas when 30 seconds remain. Drain pasta and peas and add them to the sauce.
Add the Parmigiano-Reggiano Cook and cook for 1 minute.
Serve with freshly grated Parmigiano-Reggiano and a side of Flat French Bread.