Cook linguine as per package instructions until al dente.
While pasta cooks, add olive oil and garlic to large 12-inch pan and cook over medium heat until fragrant, about 1-2 minutes.
Add cream and citrus zest, reduce heat to low and bring the mixture to a VERY LOW simmer. Simmer the mixture for 5 minutes. Add salt and herbs, stir to combine. Turn off heat and stir in cheese until melted. Toss with pasta and serve immediately.