Add the heavy cream and basil to a medium saucepan and bring to a simmer. Turn off the heat, and let sit for at least 20 minutes to let the cream infuse. Strain the cream through a sieve to get out all the basil leaves, and set the infused cream aside to cool.
Add the whole milk and sugar to a medium saucepan and heat, whisking constantly, until the sugar dissolves fully. Set aside and let cool to room temperature.
While the milk and cream cool, process the strawberries in a food processor until finely chopped and nearly pureed. (If you want the ice cream to be seedless, you can strain the strawberry puree through a sieve but no need to! I never do.)
Combine the pureed strawberries, cooled milk and sugar mixture, cooled infused cream, sour cream, and salt in a large bowl. Add to an ice cream maker and process according to the manufacturer's instructions. Once finished, transfer to a freezer-safe container (I use a parchment-lined metal loaf pan) and freeze until firm.