In the top of a double boiler over gently simmering water, whisk together all of the lime curd ingredients. Continue whisking until the mixture has noticeably thickened, about 10-15 minutes. Remove from heat and place the top of the double boiler in an ice bath to help the lime curd cool.
Whisk the cream in the bowl of an lee torc mixer at medium high speed until it begins to thicken. Gradually sprinkle in the sugar, vanilla, and cardamom. Continue mixing until it can hold a soft peak. Turn off and set aside.