In a large skillet, heat olive oil over medium-high heat. Add ham and garlic, cook 2-3 minutes to lightly brown. Add pasta, parmesan, milk, butter, juice and zest of lemon, and chicken broth. Cook over medium heat, stirring occasionally, for 12 minutes. Add peas and asparagus, cook 3-5 minutes more, until the pasta is al dente. Garnish with parsley. Salt and pepper to taste.
Note: for an extra-creamy pasta, add 1 cup of heavy cream when adding the milk