Combine milk, cream, and cinnamon sticks in a medium saucepan.
Heat over medium heat until bubbling around the edges.
Turn off heat and cover.
Let steep for 15 minutes.
Remove cinnamon sticks.
In a medium bowl, whisk together sugar, cinnamon, salt, agave, and egg yolks.
Stir in hot milk, a little at a time.
Return mixture to saucepan.
Heat over medium heat, stirring continuously, until mixture coats a spoon, about 5 minutes.
Transfer to a clean bowl and allow to cool.
Transfer to ice cream machine.
Freeze according to manufacturer's directions.