1. Bring vermouth and garlic to a boil in a large skillet over medium-high heat; reduce heat to medium-low, and simmer 7 to 10 minutes or until vermouth is reduced to 1 Tbsp.
2. Whisk together half-and-half and cornstarch. Whisk half-and-half mixture, salt, and pepper into vermouth mixture; bring to a boil over medium-high heat, whisking constantly. Boil, whisking constantly, 1 minute or until mixture is thickened. Add pepper Jack cheese. Reduce heat to low, and simmer, whisking constantly, 1 minute or until cheese is melted and sauce is smooth. Remove from heat, and use immediately.
*Dry sherry may be substituted.