Slice kernels off the corn cobs and place in a large saucepan. Break the cobs into thirds and combine them together with kernels and sugar in the saucepan.
Pour in milk and cream. Bring mixture to a boil and stir until sugar dissolves, about 2 to 3 minutes. Turn off heat and remove from the stove. Add in sprigs of basil and allow basil and cobs to steep for 1 hour.
Remove basil and cobs with thongs.
Using an immersion blender, puree the corn kernels. Pass mixture through a sieve pressing down hard on the solids. Discard solids. Cover and refrigerate for at least 2 hours.
Place frozen bowl on base of ice cream maker and turn it on. Pour chilled mixture into frozen bowl and churn until desired consistency, about 15 to 20 minutes.
If you prefer a firmer consistency, transfer ice cream to a container and place in freezer for a couple of hours.