In an electric mixer, combine the evaporated and condensed milk and whisk on high.
Pour off most of the juice from the can of peaches and place them in a shallow plate. Using the back of a fork or a knife, cut and smash the peaches up. This will release some liquid, which is fine.
Add the smashed peaches to the milk mixture and mix until combined.
Place in a container that will freeze well and transfer to the freezer for a few hours.
When you are ready to serve, remove the peach ice cream from the freezer and let soften for 15 minutes.
While the ice cream is softening, heat the grill to high. Cut the fresh peaches in half and remove the pits. When the grill is hot, place the peach halves on the grate and char for a few minutes until the fruit has softened and grill marks appear.
To serve, place a grilled peach half into a bowl with a generous scoop of ice cream.