Add cream, milk, garlic, white pepper, cayenne, lime juice and Asiago cheese, to a large sauce pot. Mix well.
Place over medium heat and bring to a light boil.
While sauce is heating, prepare the slurry - In a small container add cornstarch to water. Stir well to dissolve.
When sauce begins to boil, whisk in prepared slurry.
Reduce heat to a simmer.
Whisk Boursin cheese into sauce. Stir to combine and melt.
Once the cheese has fully melted into the sauce, remove from heat.
Allow cheese sauce to cool to room temperature, then place in a container store in refrigerator, uncovered, until chilled, stirring occasionally.
Once cold, cover and keep refrigerated until ready to use.