In a bowl whisk together the milk, cream, sugar, vanilla, and cayenne until the sugar is dissolved. Chill thoroughly. Once chilled, churn in an ice cream maker according to the manufacturers instructions.
While the ice cream churns make the purées. Combine the ingredients for the jalapeño sugar in the bowl of a food processor (I use a mini for this), and pulse until the jalapeno is very finely chopped. Set aside.
Combine the strawberries and sugar in the food processor and pulse until puréed. Set aside.
In the last five minutes of churning, add in the jalapeño sugar. I also added a pinch of couse sea salt. When the ice cream is done churning pour half into the container you intend to store it in and swirl a quarter of your strawberries into it, just swirling a bit, not turning the whole thing pink. Pour the other half on top and repeat the strawberry swirl. Reserve remaining strawberry sauce to top ice cream or for another use.
Either eat soft serve (my preference) or chill in the freezer until hardened and scoopable.